Programa

Friday, April 8, 2022

7:15 PM

 

<<2022_03_11_122009-2022__1__ELECTROTECNIA__7705__Ciappa_Pokidiuk__Pablo_Nicolas.docx>>

 

 

Clases

domingo, 9 de marzo de 2025

00:53

 

C1 - Repaso Circuitos

Monday, March 14, 2022

6:31 PM

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C2 - Circuitos

Monday, March 21, 2022

6:42 PM

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C3 - Thevenin, Norton, Kenelly

Monday, March 28, 2022

6:37 PM

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C4 - Magnetismo

Monday, April 4, 2022

6:06 PM

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C5 - Circuitos Magnéticos

Monday, April 11, 2022

6:34 PM

 

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C6 - Regimen transitorio

Monday, April 25, 2022

6:25 PM

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C7 - Corriente Alterna

Monday, April 25, 2022

6:46 PM

 

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C8 - CA Fasores

Monday, May 2, 2022

6:35 PM

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C9 - Laboratorio

Monday, May 16, 2022

1:54 PM

 

<<LAB01 - Electrotecnia Corriente Continua_Rev 0.pdf>>

 

<<LAB01 - Practica de laboratorio N1_Rev 0.pdf>>

 

C10 - Mixtos CA

Monday, May 16, 2022

6:39 PM

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C11 - Nros Complejos

Monday, May 30, 2022

7:03 PM

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C12 - Potencia CA

Monday, June 13, 2022

6:43 PM

 

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Guías

domingo, 9 de marzo de 2025

00:54

 

Guía Circuitos (Larga)

Tuesday, March 15, 2022

8:03 AM

 

<<Electrotecnia Guia 1.7 Conceptos Basicos de Circuitos.pdf.pdf>>

reabastecimiento. ¿Qué propiedad tiene el combustible? Energía almacenada en forma 
química. Durante el consumimos el combustble, obtenieMiO una rapidez de 
movimiento, una distancia recorrida V calor. Sabemos que cuanta más distancia 
pretendamos obtener con la misma cantidad de combustible, más despacio deberiamos 
desplazamos. Pero con el volumen de combustible en el tanque. sabemos que hay un límite de 
distancia que podemos llegar a Además, en podríamos aprwechar el calor 
para atemperar el habitáculo del vehículo, Pero en Verano, tenemos ningún interés en ese 
calor, y sería preferible reducirlo. Es decir que también tenemos productos deseables e 
indeseables. 
Si un volumen de agua en un recipiente a una determinada altura, podemos usarla 
para mcwer las paletas de un ventilador. Una vez que el agua llegó al nivel inferior, sabemos 
que no podemos obtener el mismo movimiento, a menos que nosotros no esforcemos y 
subamos ese volumen de agua a su ubicación iniciaL Pero estamos en el caso anterior. En este 
Caso, el fluido no sufrió ninguna transformación quimia, ni cambió de estado. Simplemente Se 
redujo su altura y, sin embargo, seguimos hablando de energia. 
Sabemos perfectamente que tenemos que estar bien alimentados si vamos a iniciar 
actividad que requiera de intensos esfuerzos. LOS nutricionistas de los de alta 
competencia Io saben muy biem De alguna manera, necesitamos tener energía almacenada en 
el cuerpo para poder comenzar, Pero esa energía no puede estar almacenada de cualquier 
manera_ Tiene que ser energía almacenada que se pueda convertir en movimiento muscular al 
momento de Ser necesario. La abdominal no Sirve a ese propósito en el caso de alta 
competencia, Oe la misma manera que tenernos energías de diferentes calidades en nuestro 
cuerpo, también disponemos de energias almacenadas que se pueden aprovechar con 
diferente de éxito realizar trabajo. 
La cantidad de energía térmica que produce un determinado combustible por unidad de masa 
o de volumen, recibe el de poder calorífico, La siguiente lista los valores de 
poderes caloríficos de diferentes elementos químicos: 
Hidrógeno: 143MJ/kg molecular gaseoso _ 
Carbcw'0: 34MJ/kg. 
Azufre. 9MJ/kE. 
Un cormbustible usado es el carbón mineral Este tiene diferentes Clasificaciones y 
calidades. Enumerados de mavor a menor en poder calorífico, tenemos: antracita, hulla, 
carbón bituminoso. lignito, V turba, 
Duro, tiene el mayor contenido carborw (llegando a 95%), poder 
calorífico de 35MJ/kg, V menor contenido en materias volátiles, Debido a Su menor 
contenido en materia volátil, resulta de ignición dificultosa. Arde dando una llarna azul 
corta y sin apenas humos Tiene una estructura cristalina y un color negro brillante. 
Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7 Hulla: Con un alto contenido de carbono (entre el y el 90%), bastantes volátiles y 
un poder calorífico que puede llegar a 33MJ/kg puede utilizarse en 
procesos de combustión y en industrias siderúrgicas. 
Carbón BitwninOSO: ES relativamente duro, Contiene entre un GO y un de carbono, 
Con resto de agua, aire, hidrógeno y azufre, De negro, a veces marrón oscuro, 
presenta vetas definidas de material brillante y de material mate. Su poder calorífico 
estaentre los 24 33 MJ/kg La hulla 
es el carbón bituminoso de mejor calidad. 
Lignito: Abundante, de color negro o pardo, y una estructura leñosa o fibrosa. 
Contiene elevada humedad V materia volátil. Al lignito negro se le denomina 
también "carbón Subbituminoso". De formación más que la hulla y la 
antracita, Su poder calorífico llega IGMJ/kg 
Turba: Geológicamente, de formación reciente. quedó en una primera de la 
transformación de materia vegetal, típicamente de zonas pantanosas. Su bajo poder 
calorífico se debe al menor contenido en carbono disponible en la combustión, y es del 
Orden de los 8 MJ/kg. 
Podemos considerar al carbón mineral como un recurso no renovable, debido a que requiere 
millones de años las plar-.tas en carbón, es un ritmo mucho más 
lento que el Can Su nivel de Consumo, aunque hay muchas reservas. 
Existe también el vegetal. que Se obtiene artificialmente quernando rnadera apilada en 
ausencia de oxígeno para que su combustión sea parcial , Es muy usado como combustible, 
debido a que tiene más poder calorifico comparado con la lena. Las pilas utilizadas para 
preparar carbón wgetal Se llaman carbmeras. 
La lena presenta un poder calorífico del orden de los IOMJ/kg. 
Ing. Pablo Ciappa ELECTROTECNIA -CONCEPTOS BÁSICOS DE CIRCUITOS vl.7 Eierck'o: El esp«ifia la ewgia a 
urntaria de una sustancia, para su temperatura 1 kelvin, Asumiendo para el agua liquida un 
de' de 4,20/kgK, V e' 'htegmmente e/ agua, 
detemiw de a g cm de O a la de huna. 
[ignita twba y wqeta' en ambustión 
En resumen, hay una magnitud que llamamos "Energía", V está relacionada en estos y en todos 
los procesos requerinu.s un minimo de esta para ejecutar la actividad, Así, uno de yos 
indicadores de nivel de civilización, es justamente el de uso artificial de la energia_ 
Necesitamos energia para modificar Objetos o Situaciones. Iluminar un lugar en plena noche, 
es un ejemplo claro. junto con la modificación de otros parámetros ambientales, tales como la 
la h'mnedad, etc. La energía que para hacer esas tareas 
generalmente está dis*anible en el lugar donde la Por ejempb, el gas que se 
usa para iluminar en campamentos suele estar inicialmente en Otros lugares, es extraído. 
almacenado en garrafas, trasladado, y luego usado. También puede ser enviado a la distancia 
por medio de gasoductos. 
El CMVcepto de la Energía requiere especial análisis, porque nos pemite establecer vínculos 
entre las distintas ramas de las Ciencias naturales la tecnología. Tan importante es, que 
desde hace años venimos estudiando diferentes métodos para usarla de manera racional, 
aprovechándola con el máximo rendimiento y eficiencia. 
El concepto de eficiencia es importante por tres 
El primero, está asociado a obtener tiene un costo asociado, el cual 
intentamos reducir _ 
El segundo, está relacionado con qué hacemos con la energía que no se emplea 
especificu-nente el buscado. general, está asociada las 
pérdidas. La experiencia que, si se queda en un punto, 
terminará elevando la temperatura de este, a Veces incluso superando peligrosamente 
los limites admisibles, 
El tercero es que el uso de la energía productos pero también 
productos indeseados. El manejo irresponsable de estos productos 
(residuos) produce severos casos de contaminación, y está tomando dominio público, 
IO que se traduce en la irnplementación de politicas de relacionadaS_ 
En cada oportunidad en que hacemos una tarea, trabajarnos. Por IO tanto, para obtener un 
producto o un servicio, ejecutamos un Trabajo. Para poder ejecutar ese trabajo, necesitamos 
pmiamente Luego de el trabajo, tend—os Así, entre 
la energía en el estado inicial el de esta en el fmal y el trabajo N 
establecer la siguiente relación: 
Esto significa que tanto la energia como el trabajo Se expresan usando la misma unidad. Esta 
es el "joule" o J. 
Hay Otro factor a acerca del trabajo, que está relacionado Con la rapidez Con que Se 
ejecuta una tarea. Podemos expresarlo mediante el tiempo requerido para hacerlo. Sin 
embargo, veces es mas conveniente expresarlo mediante la cantZad de trabajo que se 
hace por unidad de tiempo, concepto al que llamamos potencia p, Así: 
Ing. Pablo Ciappa ELECTROTECNIA -CONCEPTOS BÁSICOS DE CIRCUITOS vl.7

 

 

 

 

0 を w メ 0 一 9 n' 0 、 、 & 0 、 」 O' 0 pnb 第 、 、 0 よ 当 、 0 き 0 を ミ も 新 0 ・ ど を ・ 、 ー き 簷 : を こ ? 
0 当 こ 0 ミ 、 、 ー 00 -0 で を き き ー 0P0 一 0 を . に 0 」 き & を き を 0 」 き 0 一 0 を に に 当 0 と て を 、 と 、 0 
言 も よ ミ ・ 0 き 0 、 を 」 0 よ 寰 - 2 & き 、 、 、 第 き 0E0 一 き め -0 一 0 、 要 0 告 を p ー を を き & ま OP に を 0 、 
ま を 0 、 上 on に モ を を 、 当 き 0 ~ PO 0 、 を 0 」 き 00 - 当 を -0 を を 30 ・ と 0 、 を て 
に 0 を 、 0 0 3 物 新 0 と 0 、 日 0 し 000 日 ~ 0 、 0 0/ 0 0n60 0 ~ = 3 b 060 、 と u 、 し 0 00q 0u0 30 
【 A50 ヒ n し 30 50u 新 78 501d 〕 し 20 ー さ N 日 10 」 当 3 & 0P0 Olqed 物 」 一 
0E0 リ 一 0 一 」 0 、 030M'W 1 を に 」 { 0 0 新 と ~ ・ 0 一 0 で 0 、 OW 、 p 0 電 「 0 良 •p O) 、 つ & 、 ら と ′ に 0 い 
3 ー に 3 ー と 、 新 0 響 一 8 朝 2 を 0 、 0 一 0 ミ 0 し 0 0 さ 、 お 一 0 0 を を ~ 一 3 0 で u 製 で 、 当 を 新 製 を u30 気 を 00 当 朝 ~ 
- き 」 0 、 ・ 0 一 日 0 で を 00 瑟 u010 を を 0 き 、 32 0 ト ヨ に 01 に 0 、 0 と 新 w ョ 朝 05 新 03031 6- 製 ヒ 当 3 
- 「 0 、 04 8 ・ 0 一 u 日 0 で を 00 ~ を 0 を を 0 ま き マ 、 32 0 を ョ に 01 に 0 、 0 」 な ~ ~ w ョ 朝 05 新 030 、 16- 製 ヒ 当 3 
、 ま 108 一 - 09 05 ゞ 二 0 マ 、 OE 、 ま 0 へ 》 -- 5 「 ゝ 1 き 【 ま 3 物 新 3 、 0 お 0 、 3 36 冒 w を 一 0 
、 ま 108 、 一 - 09 05 ゝ 二 0 マ 、 OE ゞ 1 、 0 、 、 一 -5 「 、 宝 き 【 、 5 3 物 ・ 3 、 0 お 0 、 3 36 w に ロ 一 0 
0 ミ 0 第 0 、 0 ミ ト 、 ~ で 一 7 日 55 国 S 曰 曰 0 6- 凹 ョ 、 、 ) 新 薹 、 2 物 さ = 0 第 、 0 第 16 一 製 と ミ 編 
~ 0 」 0 、 、 0 産 と 、 当 b 07 、 礼 0 新 を 0 0 ~ 望 3 さ 良 3 OX き 要 0 ト 一 0 当 朝 ~ 
~ 30 よ 、 OP 当 、 を を 、 一 & [ OPOJ•• を 6 3 き 、 き 0 当 一 - OW p ト ミ [ 一 を 
3 当 0 新 0 、 0 、 0 を 物 0 0 製 - 三 6 当 当 0 し て に 3 6 、 30 製 、 0 を w 、 3 】 30 
な を に 当 ・ ま 一 00 -0 一 opuo WO と を 0 : 0 ト 0 一 こ O" を ~ & 0 一 0 を 
- 0 を を き 0 当 ~ 一 、 、 当 当 を 警 を 00 ト 、 ミ 0 一 に 0 い 6 「 
~ 0 当 -0 を 良 ミ き 3 9 、 0 き 0 良 0 導 0 き 
~ 00 に 3 、 3 当 で 3 393 で 当 当 33 と 50 当 O' 、 ~ 
ー 0 」 0 産 【 、 3 新 日 ~ = - き 9 で に ミ 0 ミ 
礼 00 に 3 、 で 日 3 き 3 
を を さ 0

 

 

 

 

 

En realidad, los electrones libres no son las únicas cargas eléctricas que se pueden mover. En 
los electrolitos de las cubas electroquimicas, se pueden mover iones, es decir, átomos V 
moléculas de sustancias, a las que les asignamos cargas de Signo positivo. En ese Caso, estas 
cargas se mueven en sentido contrario al de los electrones libres. Cuando estudiamos 
Electrónica, para comprender el funcionamiento de los dispositivos, planteamos la existencia 
de ciertas entidades llamadas "huecos" o que tienen 
carga igual V opuesta al electrón, que expresa la ausencia de 
este. Nuevamente apelando a otra analogía. sería equivalente a 
estudiar el movimiento de los pasajeros en un transporte público 
que no tiene ocupación plena de sus asientos. por diferentes 
motivts, los pasajeros Se Van cambiando de asientos. En lugar de 
estudiar el movimiento de las personas que se cambian de asiento, estudiamos "el movimiento 
de los asientos que quedan vacíos". 
La intensidad de corriente eléctrica es la cuantificación del fenómeno ya que indica 
cuanta carga eléctrica pasa por segundo por un conductor. Responde a expresión siguiente: 
Su unidad de medida sería el coulomb/segundo (CIS) que denominamos "amper", y se 
simboliza "A" _ Segun el sistema intemacional de emidades, si ape"ido de un 
científico, este se escribe en minúsculas, y sin letra "s" final. La inicial se escribe en 
may las. 
Supongamos que un capacitor almacena carga según el siguiente gráfico: 
La corriente I es de 2A. 
"Q 4C 
En este gráfico, no entramos en el detalle del porqué el capacitor Se cargar de esa manera, 
También, haber calculado el mismo valor 2A usando Otros intervalos, aunque en 
este caso, todos darían el mismo resultado si usamos partes de la gráfica posteriores al 
instante iniciaL 
Veamos el siguiente caso: 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7

 

 

 

C 【 > 50 3050U 一 S78 501d3 NOD • 之 3 081 313 Olqe-d 
0 0u0P0 一 0 u ! uap 一 10 0 」 Od ua 」 3304 0 aqap mb 0 」 0d0 
•odu•ag pp - -9 ua 8 【 r 名 
(l)od»n•puodes•d•nbaauauaoo

 

 

 

 

Eierck'o: de 
Fin de' 
Además, es importante aclarar qué entendemos por "superficies Esto es algo que 
podemos verificar fácilmente Con el Siguiente caso. En el 
esquema tenemos dos nodos. Para el nodo superior, podemos 
escribir: 
Corno conocernos todas las comentes menos 13, la 
Para el nodo infericy, podemos escribir. 
Con la particularidad no conocernos dos de las comientes 
e pero podemos decir que a una de ellas la averiguamos antes. Entonces, gracias a este 
último dato, podemos despejar que no conocemos: 
Y aqui es cuando se torna interesante el tema de las superficies, Si dibujamos una superficie 
que abarque los dos nodos (trazos finos alineados), podemos deteminar la de las 
comentes entrantes y las salientes: 
Donde encontremos que no aparece en la expresión, debido a que no cruza la superficie 
cerrada, y que la única es la corriente 
Ejercicio: qué comiente circula por el cable a de la 
"n del 
Ejercicio: que p. el a de 
13 
Ing. Pablo Ciappa 
Fin del Ejercicio. 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7

 

 

 

Fuerza electromotriz, caída de tensión y tensión eléctrica 
para que las cargas eléctricas de distinto signo se muevan en un circuito intentando 
encontrarse formando una corriente eléctrica, primero deben estar separadas. Pero las cargas 
eléctricas no se separan Tenemos que hacer algún "trabajo" para 
conseguirlo, o tenemos que conseguir que algún aparato Io haga. Por Io tanto, la corriente 
eléctrica no es un fenómeno espontáneo, Tiene que existir una causa que la provoque. A esta 
causa es IO que llamamos fem (por Fuerza Electromotriz), la propiedad que tienen las 
generadores de energía eléctrica de impulsar a la corriente eléctrica. Se representa con la letra 
E. Su magnitud se mide en V o "volt". Es importante destacar que, cuanto más trabajo 
hacemos, más se separan las cargas y, por IO tanto, mayor es el valor de la fem. 
Si pretendemos expresar esto de manera cuantitativa, debemos considerar que cuantas más 
cargas separamos, más trabajo debemos aportar. Pero, para una cantidad constante de cargas, 
cuanto más hs separemos, también deberemos aportar más trabajo. Así, al trabajo N para 
separar las cargas Q podernos expresarlo Como: 
Siendo D la distancia de "separación", y k una constante que depende del medio en que se 
separan las cargas. Cuando no nos interesa específicamente Io que ocurre dentro de los 
generadores, al producto A D lo podemos agrupar en una única que es la que ya 
hemos llamado fem E. 
Si la fem E está relacionada con la energía disponible, cuando se la aplicamos a una carga, el 
principio de consewación de la energía dice que la energía es consumida la carga_ por 
IO tanto, tendremos: 
Donde Wc es energía eléctrica consumida, mientras que es energía eléctrica generada 
Pero nosotros sabemos qiR la energía eléctrica generada Wo es: 
Por Io tanto, podemos escribir que la energía eléctrica consumida We es: 
-QE-QU 
En la expresión de la energía eléctrica consumida We, hemos cambiado a la fem E por la 
tensión V, para expresar justamente que hablando de consumo. 
Como en este Circuito tenernos que la en el y en la Carga Son *uales, y el 
tiempo transcurrido es el mismo, sus productos Son idénticos V por IO tanto, la carga que 
separó el generador Q es igual a la que atravesó la carga. Así, podemos simplificar la última 
igualdad, obteniendo: 
Esto es IO que en el esquema anterior. 
Este análisis que acabarnos de hacer presume que los conductores Son ideales, es decir, que 
toda la energía generada es gastada por la carga como energía consumida 
Ing. Pablo Ciappa ELECTROTECNIA -CONCEPTOS BÁSICOS DE CIRCUITOS vl.7

 

 

 

 

 

 

Eierck'o: En el esq— Uu y 
Ejercicio: En el siguiente esquema tres fallas de no intensicmales_ una en el 
eléctrico de y los de bs —os. entre 
(aquellas por donde circulan nonnalmente comentes) sus masas Dibujar el circuito que 
lo situación y HZ y H3 
hs de 
En el esquema anterior, el usuario Hl no Sufre ningún te, debido a que el apa rato 
ekctrko qw no de aislamim•vto. Esto significa de 
que es cero. Io tensión a que queda sometida el aislamiento de ese aparato y 
detem 
Ejercicio: de H2 y H', y e' I 
S' hs de 2 3 del qué 
tensión deberíamos planificar los aislamientos de cada uno 
Ing. Pablo Ciappa ELECTROTECNIA -CONCEPTOS BÁSICOS DE CIRCUITOS vl.7

 

 

 

 

 

 

 

 

 

 

 

 

de de 60V c.do de La 
alim enta con 220% Dibuje e' Determine el valor de resistencia serie adicional, Oe termine el 
mndimifflto del te 
Caida de tensión en cables 
Existen otras causas para que la tensión recibida por las cargas sea menos que la del 
generador. La resistencia de los conductores no Sólo produce Efecto Joule en los 
También influyen en la carga de la siguiente manera: 
Lin ea 
O, 20 municipal 
L 30 
- U.Ut-20v 
La suma de las resistencias de este circuito es entonces de 5,50, Esto hace que la comente del 
circuito ahora Sea de 40A en lugar de los 44A que había antes. 
Esto nos permite definir el concepto de caída de tensión "U. La tensión que ahora está 
recibiendo carga que es de La caida de ó','es entonces de 20V. También 
debemos evaluar Si esto es admisible para la carga. La caída de tensión admisible para las 
instalaciones de ilurninación es del 3% mientras que la caida de tensión admisible para las 
instalaciones de no son de iluminación es del 5%, En casode no cumplir con estos 
modifiar general 
esto Se aumentando la sección de los conductores, IO que produce una 
de Su resistencia. 
La caida de tensión, en Circuitos de Corriente Continua, Se calcula de la Saliente manera: 
—2p-,'-21L--21Lr 
Siendo r, la resistencia de cable de un material conductor y de una sección por uridad 
de longitud, V es un valor que aparece en los catálogos, 
En corriente alterna, la para determinar la caida de tensión es algo más elaborada. 
Pero un método Simplificado, basada en ciertas bastante razonables pero que 
aún no estarnos en posición de comprender, es el que VerernOS a continuación. Observemos 
que el valor de r, es lo que llamamos -caída" en la tabla que tenemos a continuación, 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7

 

 

Eierck'o: El est— de a a 120 
de de ene 
Estimar Ia caida de tensidn en de 'a siguiemte tabla_ 
Se caón 
caida WAkm 26 15 to 
'0 16 25 SS 50 70 SS 120 
4 '2 08 06 05 04 
Esto tabla de temión 'os de ovo de IA y 
de I km más bum de 
L , xales AEA90364-7.7n, 
Salvo información en contrario, en pomera deberruas considerar que caída de tensión U es: 
Caída x longitmi 2.4 
— x 444 x 0,12km 12,7V 
C— e' acede e' PM Io mto, Ia 
del cabJe a 25'" m', si con esta que caída de tensión sea menor que el 
Caida x x longitmi IS 
— x 44A x 0,12km - 841' ACEPrABLE 
PM si de' cable admite de obtew 
de tensión Ia in«unentamm a Cobe que no 
de Jo de En continua mia e' 
seguir, En Corriente altema„ es un paco más elaborado, ya que debemu.s el erecto de Ia 
Este método y de Io AEA 
Lo de' de 44A en debido a que 
de eVg'r el coiKide 
que Ia tensión nomina/ de Ia «d, 
EierOOo: En el siguiente esquema, Ias de 10s diemn, para el ampeánrtro 
de _5A pam 10s voltímetros, de 220v, 223", 'v 3v_ Sugerir dónde se coda 
de 'as tensiones_ e' y 'os de que Ia 
tensión de' wdstato no es igual a tens'ón de e Por qué Ias de 'os voltimerras de 'os 
E)ercizio: mide te "On de/ móstato si 
a de' sin si ? 
Fin 
CA'DA DE TENSION DURANTE EL ARRANQUE 
Algunas Cargas, en el de Ia conuión, una que supera varias 
Su Corriente de servicio. caso de IOS eléctricos: 
In'. Pablo Ciappa ELECTROTECNIA -CONCEPTOS BÁSICOS DE CIRCUITOS v1.7

 

 

 

 

 

 

 

 

 

 

en R2. Dichas corrientes I, e L son merwres que la corriente total I. Por este motivo a esta 
configuración la podemos llamar "Divisor de corriente". Determinarernos cuánto vale la 
corriente de la resistencia R': 
1,Rr• LR, 
O también: 
Considerando solo los dos miembros de la primera igualdad: 
podemos despejar h: 
ES decir que la corriente de una resistencia corresponde al producto de la corriente total V la 
resistencia de la rama opuesta, sobre la suma de las dos resistencias, 
Eierckío: si 1=24, RAO'" y RAO'". el de 
Eierckío: 'a el 
remcado a 
Cwn-ple la expresión del diWSOr de Corriente de las resistencias es nula P 
EierCtja: Si persona ma teriol CM mi Sm O conectado. 
que use de protección ¿ Que O tm5 
hacer en pretendan OS hacer que gue por pemona Sea nula P 
Fin Ejercicio. 
Ejercicio: el el 
Luego 
determinar 'a comente que 
S' es 
proponer reducir el de 
Pe 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7

 

 

 

Trabajo y Potencia eléctrica 
Hasta considerado tensónes, corrientes, resistencias V sus relaciones como sino 
existiesen limitaciones en los valores que pueden tomar. Esto no es totalmente cierto. 
Teniendo en cuenta que la energía de una fuente es: 
Y que la carga entregada por la fuente al circuito es: 
Entonces tenemos: 
por Io tanto, si la energía es consumida por una única resistencia tendremos: 
Como la potencia es la energia transferida dividido en utilizado: 
De esta manera, ya tenemos las expresiones de trabajo. 
En el caso de una resistencia, donde sabemos que se cumple la ley de Ohm, tendremos: 
Y esta potencia, multiplicada por el tiempo, nos da la energia eléctrica que recibe la 
resistencia, que es el trabajo que gasta en hacer circular la comiente, y es la energía que disipa 
en forma de 
A esto Io conocemos como efecto Joule. 
Cuando: 
A esta potencia disipada en forma de la usamos para una aplicación, la 
denominamos "potencia útil", "calentamiento por efecto Joule", o alguna frase similar. 
Cuando esta potencia es un resultado no buscado, la denominamos "potencia de 
pérdidas" o "perdidas efecto Joule". 
los valores faltan en el Cuadro; 
20 n 
2,5kw 
un de 220V 15mW_ Dibuje y el eléctrico_ 
y Jo o•wgio disipada de de —do 
a' 220V q'" el 220V? 
Eiemizio: un de 220V 15WW de de y de 
'orga Dibuje fisico y e' cim_'ito eléctrico. las y 
o' 220V que el de —do 
hs 220V a' ? 
Ing. Pablo Ciappa ELECTROTECNIA -CONCEPTOS BÁSICOS DE CIRCUITOS vl.7

 

 

 

 

 

terminales de redes de BT no superen los 50 metros de largo, V que periódicamente se 
controle su aislamiento para que su valor no caiga de que resulta equivalente a lmA, 
Si pretendernos evaluar las pérdidas en forma de calor en el aislante del cable, deberemos 
considerar: 
p U Ifuga 220V 0,44mA 0,0968W 97mW 
La mayor parte de las pérdidas de los cables se dan por efecto Joule en la parte conductora. 
El XIPE presenta valores similares de corriente de fuga para situaciones comparables Sin 
embargo, el XIPE presenta una de servicio aÚnisible mayor, y menor constante 
dieléctrica. 
Los materiales metálicos que no conducen comente eléctrica en sewicio normal tienen como 
objetivo proteger mecánicamente al y al aislamiento que lo rodea, blindaje para 
interferencias electromagnéticas V eventualmente, para evitar puntos alta concentración 
de campo eléctrico que derivaría en puntos de falla del aislamiento del cable. 
Los cables para instalaciM1es eléctricas son tramos conductores famados por varios 
filamentos de alambres finos paralelos, que la mayoría de las Veces están rodeados de por IO 
menos una capa de material aislante. 
En la actualidad, los conductores monoalambre no se emplean en instalaciones eléctricas. 
El Objetivo del material conductor central es llevar comiente eléctrta longitudinalmente. 
El objetivo de los materiales aislantes es de evitar ("reducir al minirno" seria más adecuado) las 
fugas de corriente en forma transversal. 
En ocasiones, puede estar rodeado de dos o más Capas o estratos de materiales aislantes: 
El aislante que rodea al conductor es básicamente el encargado de evitar las fugas, y Se aplica 
por extrusión durante la fabricación, 
En cambio, estratos aislantes exteriores muchas veces se aplican por fajado, y sirven para 
mantenerlos agrupados y como protección contra agentes externos (químicos, radiación 
ultravioleta, etc.), mientras refuerzan el aislarniento 
También pueden presentar una capa de material conductor entre las capas aislantes, que Sirve 
de protección frente a agresiones mecánicas, pero también para canalizar corrientes de fuga 
evitando que Circule por lugares en donde podrían generar algún tipo de pel*ro: 
Los conductores que llevan energía eléctrica se instalan de diversas maneras, Tenemos: 
Ing. Pablo Ciappa ELECTROTECNIA -CONCEPTOS BÁSICOS DE CIRCUITOS vl.7

 

conductores suspendidos en el aire que pueden ser soportados por medio 
de aisladores abajo a la izquierda, conductores "preensamblados" 
soportados sobre pared, aunaue abajo a la derecha los vemos soportados en poste. 
Corriente en cables 
Cuando la corriente eléctrica circula tenemos efecto Joule y se calientan. A mayor intensidad 
de corriente, nivel de calentamiento_ En los cables, no podemos que las 
alcancen cualquier valor, porque afectaria a las vainas aislantes que los o 
a las estructuras de los aparatos a los que están conectados. Por motivo. los cables tienen 
un valor máximo de corriente que llamamos corriente admisible I'. La corriente máxima que 
admite un cable en foma pemanente depende de varios factores: 
De la potencia disipada efecto Joule V, por IO tanto, de la resistencia V más 
específicamente de la sección transversal del cable. 
De la temperatura del ambiente que IO rodea. Por IO tanto, de la presencia de Otras 
fuentes de calor en Sus proximidades, incluyendo Otros cables, 
Del material aislante que lo recubre, que define el limite admisible, 
De la aptitud del entorno del cable para evacuar al calor, 
Teniendo en cuenta esto, en la Reglamentación de Instalaciones Eléctricas en Inmuebles, 
Oficinas y Locales unitarios de la Asociación Electrotécnica Argentina, consideran 
de la sección de los cables por medio de unas tablas que simplifican el proceso. Nosotros 
presentaremos aquí un metodo que es exactamente el que presenta la AEA. Va que tiene 
en cuenta las mismas causas de influencia, pero con un procedimiento distinto. 
Algunos de los donde estarán instalados los cables se pueden clasificar en: 
Es uema 
Descr ión 
Cables monoconductores Con aislamiento, en tubos 
empotrados en paredes aislantes. 
Cables multiconducotres Con aislamiento, en tubos 
empotrados en aislantes _ 
Cables can aislamiento, en sobre 
pared, o empotrados en pared de mamposteria. 
Cables multiconductores Con aislamiento, en tubos 
pared. 
Cables multiconductores directamente sobre la pared. 
Clasificación 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7

 

Cables multiconductores separados de la pared mayor a 
0,30.. 
Cables enterrados 
Cables multiconductores al aire libre 
Cables monoconductores al aire libre 
El método empleado es el B. 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7 Teniendo en cuenta el método de las corrientes admisibles de los cables no 
entenados son las siguientes: 
89 
76 
299 
259 
60 
319 
430 
26 
28C 
ggo 
ggt 
63 
85 
2Sg 
gg 
195 
2gg 
tt9 
6to 
100 
127 
g6E 
120 
t 61 
575 
SO 
Esta tabla está basada en "Electricite professionelle" — M. Vial —Ed. Nathan) 
¿Qué Corriente admite un cable de cobre aislado en PVC de Si el 
de XEPE ? ¿ Cadies s' de de 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7

 

Para cables enterrados: 
Cuando los conductores Son enterrados en conductos. debemos aplicar un factor de 
corrección igual a para determinar la corriente admisible, 
Esta tabla está basada en "Electricite professionelle" — M. Vial — Nathan) 
Como Vemos, estas tablas tienen en cuenta la sección de los cables, y Si estos Son mono o 
multiconductor, A estos valores debemos afectarlos por coeficientes que tienen en cuenta 
Otros factMes de 
de 
Cables "wltitonductore-s en «npotrados en 
aislantes 
Cabl« directamente en 
Cables multiconductores 
Es en 
Cables o multiconductores Con o Sin protección mecánica 
com lementaria 
0,80 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7 Para tener en cuenta la influencia de la temperatura circundante al cable, tenemos la siguiente 
'e m o "*lo FI métodm d O 
Ejercicio: ¿A qué o la tabla no es hacer come-cción 
por tempenatwa 
¿A qué del Suelo tabla que no es hacer una 
por temperatwa 
¿PO r que para mismo Cable en no entenado, e/ coeficiente de corrección por tenwatura es 
que el coeficiente que e' cable en ternado ? 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7

 

 

 

Disponemos de valores menores a IOA pero se usan como componentes internos de 
equipamientos, Como ejemplo, mencionamos al circuito de auxiliares de celdas de MT, 
Arriba de los umbrales de actuación Son ajustables, a valores inferiores, llegando al 
Normalmente, para una corriente dada. tenemos que elegir la sección adecuada. Entonces, Io 
que tenemos que plantear es: 
Esto tiene en cuenta que, para asegurarnos que el cable que estamos eligiendo es protegido 
por el interruptor que seleccionamos, deberíamos comprobar que la curva bt de actuación del 
interruptor quede entre la curva de la c:orriente de servicio de la carga, y la de corriente 
admisible del cable. 
Ejercicio: pana alimentar una carga de determinar sección transversal de cable trifásico 
de con en PVC„ instalado ti" 
de dos de atm, en w»biente a 'S 'C. 
el de 63A. 
Segán ja de m s tahOón &g'da E, tendremos los s" uientes factores: 
FI 
F2 a 79 45'0 
F3 0,87 405 circuitos en bandeja 
F' 0.80 hs 
Entonces, elegir comente admisible supere los: 
elegir cable admite te de ISA wqún 3. E' cable de 
de abre con aislamiento en PVC de soporta en esas 
te de 126A 
Antes de finalizar esta discusión, debernos remarcar que queda comprobar que el 
interruptor elegido proteja al cable contra sobrecargas V cortocircuitos, V Si la protección es 
capaz de actuar rápidamente frente a la corriente de cortocircuito minima. Luego, queda 
comprobar si el una de en micio si una caida 
de tensión en aceptable. Todas estas instancias pueden hacer que Sea necesaria 
incrementar la sección del cable, aunque en algunos casos, tenemos Otras opciones, 
Este valor Emite de corriente admisible en los cables está relacionado a los fenómenos de 
reblandecimiento o de carbonización de los materiales aislantes, Toda corriente que supere 
Si Se deja circular el tiempo suficiente, es destructiva, A mayor valor de corriente circulando 
por el cable, más rápido dañará el aislamiento, Si este es el caso, se vuelven conductores; y por 
IO tanto tendremos también Cortocircuitos y incendios. 
Para simplificar, supongamos que en nuestra instalación tenemos un único de material 
aislante. En el siguiente en de representar la temperatura r, el 
salto térmico S tomando como a la ambiental Cuando la temperatura del aparato 
es la misrna que la del arnbiente„ el salto térmico es Cero, y es el punto desde donde arrancan 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7 electrodos ubicados uno a la cabeza de la tabla y el otro al pie. Así, si lográramos implementar 
un elemento Litio-Flúor, dispondríamos de un elemento cuya fem seria de 5,92V (Que sale de 
hacer la Siguiente resta Con los valores del flúor y de litio respectivamente). 
No disponemos de este elemento. debido a que es bastante difícil almacenarlos en un 
recipiente sin que reaccionen entre si o con su entorno produciendo un agotamiento del 
elemento (aún Sin usarlo). 
El primer elemento práctico, fue el elemento Daniel, con electrodos de cobre y zinc, el cual 
entregaba una fem de I, IOV (Que sale de evaluar que son los valores de los 
potenciales electroquimicos del cobre V del zinc respectivamente). 
Si tenemos el elemento aislado, para que el electrodo de cobre sea tiene que ceder al 
electrolito de carga negativa, mientras que para que el electrodo de zinc sea 
negativo tiene que ceder Cargas positivas al electrolito, El electrodo de zinc hace esa tarea 
cediendo átomos de zinc al electrolito, erosionándose. 
Si a un elemento Daniel CLEZn le conectamos lámpara incandescente de 1,2V nominales, la 
misma brillará debido a la circulación de corriente. A continuación, Veremos que el brillo Se irá 
atenuando gradualmente, hasta que la lámpara deja de brillar. También, notaremos que 
alrededor del electrodo de cobre se formaron burbujas (de que forman una serrte 
de capa aislante A este proceso lo llamamos "polarinción". 
Si disponemos de una cuba abierta una varilla de Vidrio, podemos agitar el ekctrolito 
alrededor del electrodo de cobre y entonces, la lámpara volverá a brillar hasta que se atenúe 
nuevamente. Al agitar el electrolito alrededor del electrodo de cobre, removiendo las burbujas 
de hid"5geno que aislaban, hicimos un de una parte 
de la de pilas V baterías consiste en encontrar mecanismos de despolarización 
que no requieran de nuestra intervención. 
Cuando el electrodo de zinc se termina de erosionar, decimos que se "agota", 
Debido al electmlito liquido, el ekmento Daniel no era portátil. 
Una alternativa que Se difundió fue el elemento Leclanché de carbón•zinc 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7 Estos elementos entregan una fem de 1.50V (Que sale de hacer que son los 
valores de los potenciales electroquímicos del carbono y del zinc respectivamente, aunque el 
carbono no aparece en la tabla anterior): 
Estos elementos presentan una tensión de 1,35 a 1,7V cuando son nuevos. A IO largo 
de su vida útil la tensión se va reduciendo gradualmente, V consideramos agotados 
cuando la tensión Cae a 0,7SV, NO es e*actarnente un elemento de tensión fija. 
Notemos que consideramos en este caso, una descarga en 8 horas, con una corriente 
que resulta de hacer el cociente de la cargabilidad dividido 8 hcwas justamente, 
El electrolito es una sal de cloruro de amonio CINH„ por Io que se las conoce como 
elementos Además, al electrolito se lo vuelve espeso mediante el 
de harina o permitiendo que Sea portátil, 
Al igual que en el elemento Daniel, el carbón entrega electrones al electrolito, se rodea 
de burbujas de hidrogeno V se polariza. Es este motivo que al electrolito se le 
adiciona además dióxido de manganeso Mn07, El de manganeso cuando 
encuentra al hidrógeno alrededor del electrodo central de carbón Se combina 
formando oxihidróxido de manganeso MnOOH y despolarizando el elemento, 
La de estos elementos es el mismo electrodo de zinc en forma de que 
contiene todos comW)nentes, El problema es que el mismo electrc•do de zinc se 
erosiona a medida que se usa, por Io que, en algún rnomento antes que se termine de 
agotar, se y permite la salida de parte del ekctrolitm Quin icamente 
ese electrolito es bastante agresivo, pudiendo llegar a dañar severamente al equipo 
donde estaba siendo usado. A ese proceso se Io llama "sulfatar" el elemento, 
no desde el en Se 
fabrican, el electrodo de zinc comienza a erosionarse, aun cuando no los estemos 
empleando. A este proceso Io llamamos "autodescarga-, que los vuelve inutilizables en 
dos o tres años. 
LOS elementos primarios actuales tienen una estructura bastante elaborada: 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7 p % del anteriw, mt'dad s m w' a de 
Wh A ' «rigua,• el costo total, y con el costo del k Wh de empresa distribuidora de 
mgia S" a/ mp«to, 
Ejercicio: E' 
de u nidad de y 
de de 
de y 
tecnologías que permiten; a' menor volumen; 
Fin 
Otro aspecto a tener en 
cuenta en las pilas y 
baterías recargables, y 
acumuladores, es la 
cantidad de recargas 
admisibles. En el gráfico de 
la derecha, si descargamos 
la bateria un tenemos 
la posibilidad de obtener 
unos ciclos. 
Si el elemento es de IOWh 
nominales. en cada 
descarga obtendremos un 
20% de ese valor, es decir, 
2WW con ciclos, 
dicho elemento entregará. 
a Io largo de su vida unos 2Whx30000-600Cx)Wh, 
Nickel — Hierro 
Ni-MH 
Ing. Pablo Ciappa 
plomo.ácdo 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7

 

 

Eiemicjo,' pm' os d. de temida, qué igw' 
¿Qué s' m la pw el tiempo 
en descargarse los 
Ejercicio: de igwl y 
Demostrar q ue esta configuración tiene mejor rendimiento que un elemento cargab"idod sea 
de 
Las de agruparniento en paralelo Son las siguientes: 
Debemos conectar entre si todos los positivos de los elementos, y lo mismo debemos 
hacer con los negativos _ 
Las tensiones de los elementos deben ser iguales o muy similares. En caso contrario, 
aparecerán comentes entre los elementos. Estas comentes son 
perdidas. Además, los elementos de menor tensión recibrán una corriente 
de carga que Sólo admitirán aquellos que sean recargables. 
Como las resistencias intemas terminan siendo proporcionales a la 
cargabilidad nominal, los de menor resistencia interna tendrán mayX2res 
corrientes, que los descargarán rápidamente, Por lo tanto, conveniente que 
todos los elementos sean de la misma cargabilidad. 
La tensión resultante será aproximadamente igual al de las tensit"nes ndividuies de 
cada elemento_ Más adelante Verernos que la resistencia interna resultante, será menor que 
las resistencias internas individuales y, si los elementos son iguales, basta con tomar el vahrde 
la resistencia de uno de ellos, y dividirla por el nómem de elementos en La 
cargabilidad del conjemto será la suma de las cargabilidades de los elementos individuales 
Cuando Se agotan los elementos, Se reemplacen todos ellos. Si Son recargables, podrán volver 
a utilizarse luego de recargarlos a todos ellos. 
VearnOS ahora los elementos en El Objetivo es tensión mayor a 
la que Va tenemos, De hecho, Se surnan, Si están convenientemente conectados. Pero tenemos 
otras particularidades: 
Si bien perlemos dos pdas de 1, 5V en Serie. ¿ qué negar a Obten 
mie están Ja 
durante mismo tiempo Si el tiene doble de cargabi'idad Con prime ro, ¿ Cuál 
ago ta ? 
Fin Ejercicio. 
DOS elementos en Serie están atravesadas la misma corriente, durante el mismo tiempo. Si 
el e' doble de e' agota 
Fin Ejercicio. 
¿podemos poner dos elementas en serie de distintas tensiones 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7

 

Las condiciones de agrupamiento serie de los elernentos químicos las siguientes: 
En conexión Serie, debemos conectar el positivo de un elemento Con el negat"O del 
siguiente y así sucesivamente. 
Si conectamos elementos en serie, la tensión la resistencia resultantes serán la suma 
de los individuales. Coma todos los elementos serán a la 
misma corriente de descarga. la menor cargabilidad definirá la del conjunto. Entonces, 
la cargabilidad los elementos deberá ser la misma, para que todos se 
aproximadamente en el mismo momento, 
La recomendación por seguir es que cuando se agotan bs elementos, se reemplazan 
todos ellos. De no seguir esta recomendación, el reemplazo de los elementos se 
tornará caótico e impredecible. Si Son recargables, podrán a utilizarse de 
recargarlos a todos ellos. 
La resistencia eléctrica representa el nivel de oposición de un Objeto de dos terminales a la 
Circulación de corriente eléctrica, Se mide en Observemos que cuando la unidades 
en homenaje a una figura destacada en el área de estudio, o escribimos el símbolo en 
mayúscula, o escribimos su apellido, minúscula y en singular. 
Las resistencias se miden o con "puentes de medición" mención en 
contrario, el Circuito debe estar des energizado para hacer la medición de resistencia, De 
hecho, para medir la resistencia de un componente, dicho componente deberla estar 
desconectado del resto del sistema. 
Hay varios simbolos asociados a las resistencias: 
Res iste ne a fija 
Resistencia dependiente 
Resistencia ajusta b k 
de variable fisica 
¿Cómo deterrninamos el de una resistencia? 
Si los datos de partida son magnitudes eléctricas, %'demos calcular la resistencia usando las 
siguientes expresiones: 
LOS a utilizar para hacer los Cálculos Son los que a la resistencia en Sí, 
Esto pare•te Obvio, pero hay que tenerlo en cuenta cuando hablamos de en serie 
o en paralelo. 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7

 

 

En el gráfico de la derecha, vemos que un valor 
limite de potencia disipada puede cumplir 
Con Varias combinaciones de valores de 
Uy corriente I, que forman una hipérbola. Pero 
a su vez, los valores de tensión U y corriente 
de una resistencia R están relacionados por 
medio de la lev de Ohm. En el gráfico de la 
derecha vemos las situaciones límite de dos 
resistencias R, y otra R, de valor. 
Si los datos de partida son sus dimensiones 
físicas podernos calcular las resistencias por 
medio de las siguientes expresiones: 
R po(l + aoo)- 
La expresión primera indica que la resistencia aumenta su valor con la longitud, y disminuye su 
valor con la sección Su valor también depende del material con está construida, por 
medio de una cantidad que llamamos resistividad p_ La seomda expresión es válida si la 
resistividad depende linealmente de una magnitud física O, por ejemplo, Si Se incrementa Con 
la temperatura t (en este caso. reemplazamos e por t), 
También la frecuencia a la que hacerrK2S trabajar a la resistencia. 
que la ccwiente en una resistencia circula repartida unifomemente la 
sección del alambre, Sin embargo, a frecuencias elevadas, la Corriente circula Con mavor 
concentración (O densidad de corriente) por dentro del alambre, pero cerca de la superficie 
exterior del misn-m A esto IO dencmnamos "efecto pelicular* o "efecto skin" 
Gráfico de R vs F 
LOS resistores son los dispositivos prácticos que presentan resistencia como pri n cipal 
propiedad A puede ser usu más para 
estudiar los efectos del resistor en los circuitos eléctricos: 
De esta manera, tendremos en cuenta que la resistencia transforma energía eléctrica 
en térmica, Sino que también produce campos magnéticos y eléctricos a Su alrededor. 
Cuando se solicitan comercialmente, los resistores se especifican por: 
ValM de la en Ohm, y la tolerancia del % O ppm, 
La potencia que es capaz de disipar. 
La te C Mlogía de fabricación 
Resi fijas: 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7 Resistencias de alambre: Fueron las primeras en 
implementarse, Se arrolla un alambre metálico 
(Constantán, Manganina, Cromo•NiqueI, Cobre, o 
Aluminio) alrededor de una estructura Ciündrica 
aislante, Este cilindro puede ser macizo o tubular, de 
material cerámico o aislante. Se cubre con una pelicula vitrificada de esmalte 
que le da estructura protección, y en los resistores de alta potencia, Se IO 
rodea de cementado V estructura que facilita la disipación, que puede Ser 
cerámica o de aluminio, A estar enrolladas, presentan valores de inductancia 
no despreciables. 
Resistencias de carbón compactado: Fuerc"l las 
primeras resistencias que se hicieron para uso 
comercial masivo. Se tomaba una masa de grafito y Se 
compactaba en cilíndrica de tal que 
una sólidw Al no ser bobinadas, 
no presentaban efectos inductivos, Luego se hicieron 
llenando un tubo cerámico Con grafito IO cual mejoró la calidad de estas. 
PmdKen mucho ruido, por son para sistemas de alta 
fidelidad, 
Resistencias en pelicula de carbón: 
Depositamos una fina Capa de carbón 
orden de IOnml sobre un cilindro cerámico. 
Luego se colocan las cazoletas Con 
los conductores extremos. Para ajustar el 
valor, por medio de una púa que Se desplaza 
lateralmente, Se le da a la película de 
un trazado helicoidal que alarga el camino que 
debería seguir la corriente. Finalmente, Se le 
pone una laca ignífuga aislante protectora, y 
las bandas del Código de colores para 
identificarla. 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7 La imagen anterior a la derecha, en particular para resistencias de IO a 1000hms nos muestra 
que para una tolerancia del 20%, los valores comercialmente cubren todos los 
valores posibles 
Si necesitamos una resistencia de 740hm, podemos elegir: 
una de (684/ aceptando que *2-demos encontrarnos con cualquier valor 
entre 54,4 V 81,2 Ohm. 
una resistencia de aceptando que podemos encontrarnos con 
cualquier valor entre 61,2 y 74,8 ohm. 
o una resistencia de aceptando que podemos encontramos con 
cualquier valor entre 71,25 y 78,75 ohm. 
Si necesitarnos un valor de resistencia especifico no disponible comercialmente, podemos usar 
resistores ajustables. tema que Verernos a continuación. 
Algunos links interesantes para consultar son los siguientes: 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7 Vei•cióa 
Incluso existen algunos del giratorio cuya variación de la resistencia con el ángulo es 
sinusoidal o sinusoidal Se usan de a dos, coaxialmente, uno de cada tipo, para 
sistemas de detección de ángulo de giro, 
tenemos en fomato *electrónico", donde a la variación, en 
lugar de hacerse por medio de eje o mecánto, la simulunos 
por medio de una tensión aplicada en un terminal. 
En el siguiente link podemos encontrar información al 
Generadores de come nte 
La siguiente es una foto de dos fotodiodos, A la derecha 
vemos sus curvas 
caracter'ticas. Para un nivel 
de especifico, su 
corriente es prácticamente 
constante, Por IO tanto. 
de Comente 
para distintas 
podemos ccmsiderarlos como generadores de corriente. 
Conceptos básicos de mediciones eléctricas 
300 lx 
Las mediciones eléctricas, consisten en agregar instrumentos de mediciones a Eos circuitos, con 
el Objeta de afinar nuestro Conocimiento de IO que está Sucediendo en él, a de confirmar los 
valores que estirnamos previamente, Esto es algo muy importante que tenemos que destacar: 
No debemos bajo ningún motivo, un instrumento de medición en un sistema para 
tomar conocimiento de lo que está sucediendo. Siempre debemos tener una noción previa de 
IO que nos encontraremos. 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7 Eierck'o: el 
Determinar la intensidad de corriente que circula. 
¿Que falta que "ntido 
¿ Cómo p-cva sabe* si en e' circuito circula realmente la comente 
¿ Que si lo en om«sto o ' 
Ejercicio: para e' circuito anter"r, ¿que tensión tiene la resistencia ? 
nos falta para saber qué sentido tiene? 
¿ Cóm si e' 'a temió" 
pasa en •.ottimetro s' tensión estó en sentido opuesto a' supuesto? 
En e' hemos agmo do de Sin indicar qué magnitud 
Con mJoro Jo es de ZA, Sabiendo 
mie 'a mim V que dos componento en la 
dibujw el imumdo o nto a msi5tewiw 
ser de los aparatos de medición en cada caso 
para no del Circuito? 
Indica r g ue instrwnentO o Amperitnetro) estamos conectaMo en cada caso 
V qué 
a un pwa 
LOS instrurnentos de medición reales, cuando Se les aplican tensión, toman corriente. ES decir 
que Se Comportan Corno Las de los instrumentos que están conectado 
en Serie deben Ser pequeñas, mientras que las resistencias de que están 
conectados en paralelo deben ser muy grandes, ¿Contra qué deberíamos comparar la 
resistencia interna de un instrumento de medición real? Esta cormparación la debemos hacer 
Contra la resistencia que estamos considerando como carga. 
de V 
¿Qué p mía s' 'o al Jo q— 
Ing. Pablo Ciappa ELECTROTECNIA -CONCEPTOS BÁSICOS DE CIRCUITOS vl.7 Eierck'o: medir digital. de la 
'«tura la de 'a medición. el 
de tabla a 
I I Ramee 
Accuracy 
I a.aal 
1 voltage I 
I Not applicable 
Eierck'o: ¿Qué la Not apláable" de' 
Rp 
Lea 
: Cmdo a 
Sin emtwqo, en cm también 
misten cia y m' timetro 
c.er 'o : 
Rp VI — [«t V2J/L«t V2 
hn del 
Ejercicio: una fo ma de evitar que persona quede electrizada s' hoce contacto con &mentos bajo 
tensión, es poner copa de material aislante en el piso y las paredes. Sin este tipo de 
soluciones suele pemití' de cargas por tanto, pueden des tru" 
compon«ltes de equipos electonicos ta' e' piso totalmente 
optmdo pw otro que resulta "disipativo" de cwgas. S' e' paso es aislante, tiene que 
presentar resistencia de más de 50kn S' e' piso es disipatK•o de las cargas eléctricas, tiene que estar 
entre 50kC2 y a MO. 
En la reglamentación pa eléctr'cas se a•dm'te 
de de piso aislante que 
esta cm de de 
En m'idad, uwem 
e' dos La es 
medición y tierra Gue "amaremos VI, ta 
comiste en e' entre 
y apoyada en pisa 
un tropo y 
750,V 
PMa e' de 'a de y de 'SON 
(E' equival en te persona), un esquema de S'tuacón, y demostrar la 
del Rx 
diem: 
LM VI z 220V, V2 = 15", y = el qué e' 
¿ impl—ta? 
Ing. Pablo Ciappa 
mn del 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7 Principio de 
A modo de ejemplo, vamos a resolver el siguiente circuito por el principio de superposición. 
Aplicar el principio de superposición, implica resolver el circuito analizando el efecto de cada 
generador por separado, y luego superponer los resultados parciales para ver el resultado 
final. Para ello, debernos "pasivar" todos los generadores menos uno V resolver el Circuito 
resultante. A continuación, "pasivamos" el generador que había quedado actiw:», "activamos" 
un generador de los que habían quedado "pasivados", y resolvemos el circuito resultante. Así, 
continuamos hasta que todos los generadores del circuito fueron activados, lo menos una, 
V a IO Surno Vez, 
Para resolver el circuito, debemos primero identificar los sentidos que consideraremos 
positivos de todas las magnitudes que vamos a calcular. 
Y con estas referencias, deberiamos llenarla siguiente tabla: 
Gen. Att. E: 
TOTAL 
Y de mulera las tensiMnes y todas las comentes de cada uno de los 
del Circuito. Antes de embarcarnos en el llenado de toda la tabla, primero 
analicemos si podemos anticipar algunos resultados sin tener que hacer cálculos, y si 
realmente es necesario completar toda la tabla para poder resolver el circuito, Veamos el caso 
del Ez: está Pero el resultado final tiene que ser 
también -41'. Evidentemente tiene que entregar OE cuando está "pasivado". 
Gen. Act. Ez 
TOTAL av 
La única forma de asegurar esto es reemplazando al generador E, por un cortocircuito (cable) 
Cuando está "pasivo" y así entrega OV. Así, está actiw en generador de Comiente el 
Circuito que tenemos que resolver es el Siguiente: 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7 Así, podemos resolver el circuito parcial: 
Y completamos parcialmente la tab'a: 
Gen. Att. E: 
TOTAL 
Veamos el caso del generador Ó: Cuando está activo, entrega Y el resultado final tiene 
que ser también 'A. Evidentemente tiene que entregar OA cuando está "pasivado- 
TOTAL 
La única foma de asegurar esto es reemplazando al generador por un circuito abierto 
cuando está "pasivo" V obtener 04 Asir cuando está activo en generador de corriente Ez, el 
circuito que tenemos que resolver es el siguiente: 
Así, podernos resolver el circuito parcial: 
20 
Y completamos totalmente la tabla: 
R, 
4/34 
Gerv A ce 
TOTAL 
av 
En realidad, si observamos el cuadro, entre UR, e o entre e tenemos la ley de Ohm. 
SI averiguamos una de las magnitudes, ya tenemos la Otra, Sin necesidad de calcular todos 
valores parciales. Por IO tanto. dejamos las columnas de las corrientes. 
Además, eliminarnos las columnas de los generadores. 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7 Eierck'o: el el de s 
y las totales 
Verificar la aplicabilidad del principio de supermskión con las 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7 AN EXO: Aplicación de los circuitos serie paralelo para la comprensión de la protección de las 
personas en sistemas de distribución y las posibilidades de elección del sistema de 
Sistemas de distribución eléctrica aislados 
Los primeros emprendimientos de distribución de energía eléctrica fueron si Eos 
comparamos Con los que tenemos habitualmente hoy día, En los inicios, teníamos un 
generador eléctrico, alimentando a ciertos consumidores que estaban en su vecindad. 
En este esquema mostramos: 
Al generador de energía eléctrica, 
dos unidades con sus consumos y sus medidores de energía eléctrica consumida, 
V cables o ccmductores de interconexión, 
A estos sistemas los llamamos aislados, debido a que no tienen ninguna conexión entre las 
partes activas (aquellas que llevan y tierra. 
el primer esquema que mostramos, conductwes tienen distintas 
transversales, LOS que tienen mayor sección transversal, Son aquellos por los que circula la 
mayor intensidad de corriente, Por Io tanto, los conductores que salen de la planta generadora 
son de la mapr sección transversal, ya que conducen la corriente más intensa, 
En cada dmicilio, dM1de la eléctrica, (los 
conductores que conectan al medidor de energía eléctrica), que distribuye la energía eléctrica 
por dentro del local. Esta derivación, está ejecutada con conductores que conducen menor 
corriente y, por Io tanto, son de menor sección transversal. 
En condiciones toda corriente eléctrica sale del positivo del generador, circula por 
cables, atraviesa la carga, y por medio de otros cables vuelve al generador, por lo tanto, para 
estos circuitos podemos aplicar los métodos de resolución de circuitos serie-paralelo. 
Cada aparato que consume eléctrica requiere de un par de conductores que IO 
alimentan, Como estos conductores manejan menor intensidad de corriente que el resto del 
circuito, son de menor sección transversal aún. Todo esto que acabamos de indicar, lo 
represent*nos Con el grosor de los tratos de las líneas_ En los planos eléctricos, usaremos 
Ing. Pablo Ciappa ELECTROTECNIA -CONCEPTOS BÁSICOS DE CIRCUITOS vl.7 En el siguiente esquema indicar la corriente que produce el calentamiento indirecto es la de 
carga mientras que la corriente "de fugas es la que produce el calentamiento directo. 
La comente de fuga circula exactamente donde está dibujada. En condiciones 
normales está distribuida por todo el material aislante. Pero la representamos como Si 
estuviese concentrada, para simplificar el esquema, 
En los conductores. habitualmente la corriente de carga es la que produce la mayor porcón 
del calentamiento, siendo la segumda causa más importante el ambiente. El calentamiento 
debido a las corrientes de fuga no es de importancia en condiciones normales de servicio. 
Cuando el conductor sufre una agresión mecánica focalizada en un punto, es posible que los 
alambres conductores se acerquen a una distancia menor, produciéndose un donde la 
corriente de fuga Se irxrementa notablemente CMnparado Con el resto del conductor. 
Se ha comprobado experimentalmente que, en esos casos, Si un material aislante es 
atravesado por una corriente de fuga concentrada de 500mA, es posib•le que el calentamiento 
concentrado pueda llegar a producir un incendio del material aislante. 
Resistencia que presenta cuerpo humano 
La gráfica de la derecha muestra valores 
de resistencia medidos en los seres 
EierOOo: te circula por el c uerpo 
entre tensión 
de de 24", de SOv, de nov y de ScXW? el 
grófko de 'EC 60479 evaluar el de lo resistencia 
del cuerpo a emplean 
del 
podemos concluir que es muy dificil encontrar dos 
personas Con el mismo valor de resistencia eléctrica. 
Según e' 
siguiente 
¿qué p..to el c 
de "dido otm? ¿qué 
pre-mnta e/ de 'o los pia 
mno? En dos 
pmdKi'ia e' efMo hs de Ja 
Ing. Pablo Ciappa 
Fin del 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7 produzca su contacto directo, se establecerá una corriente que los atraviese a los dos. Corru) 
vimos anteriormente, si esa corriente supera los 30mA, representará un serio peligro para las 
dos personas. Por IO tanto, Verernos cómo hacemos para estimar el valor de la corriente de 
defecto b. 
Para simplificar, consideremos despreciables las resistencias de los conductores. Elcircuito 
eléctrico que obtenemos es el siguiente: 
El primer circuito que dibujamos nos tiene que *rmitir encontrar todas las corrientes que 
planteamos en el esquema original. El proceso de simplificación posterior no tiene por qué 
cumplir este requisito, pero el primer circuito si o sí tiene que cumplirlo. 
Vemos que la corriente sale de aplicar directarnente la ley de Ohm, al igual que la corriente 
L. Pero Io interesante es que la corriente de defecto L también. Sólo debemos tener en 
cuenta el valor de la resistencia de los cuerpos de las personas involucradas más la 
resistencia del tramo de tiewa Rr atravesado entre los pies de las dos personas. 
Asi, las expresiones que nos permiten resolver este circuito son: 
REG RT R 
Si la tensión de la red es de 220V, las tienen de resistencia y la tierra 
pmu-lta una de la de defecto de 100mA. Este valor, 
sabemos que resultará mortal para las personas. Si buscamos en la curva tiempo en función 
de la corriente que vimos anteriormente, para 100mA encontraremos que: 
En llegamos al umbral de na soltar _ 
En 5CX)rns algunas personas comenzarán a sufrir fibrilación ventricular. 
En IS el de las personas que estén en esta situación sufrirán fibrilación ventricular. 
En 25 el 50% de las personas que estén en esta situacón sufrirán fibrilación ventricular. 
Como en 0,2segumdos rw dejar de deberemos los medios 
para que el circuito Se desconecte en forma automática. 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7 domésticos, debido a que estos están prohibidos en esos ámbitos por la Reglamentación de 
Instalaciones Eléctricas en Inmuebles, Oficinas y Locales unitarios, AEA 90364-7-771. 
Un "interruptor automático diferencial" es un interruptor autotmático al que el fabricante le 
agregó un sistema de detección de la diferencia de la totalidad de las corrientes que entran y 
de las que salen, Por ese nu)tivo, son de al menos dos polos. El umbral de disparo se denomina 
"sensibilidad" LOS valores de sensibilidad disponibles pueden Ser de 10mA, de 30mA, de 
WJmA, de 300mA y de IA. Podemos encontrar otros valores, pero estos son los más 
habituales. Los de sensibilidad IO y 30mA, son de actuación instantánea. Los de sensibilidades 
mayores, pueden ser de actuación "instantánea", pero también de actuación 
demorada según los requerimientos de la instalación. En este caso el calibre del interruptor 
sólo indica el limite garantizado de calentamiento normal del aparato, y no tiene ningún tipo 
de protección propia contra cortocircuitos y sobrecargas. Por Io tanto, debemos tenerlas en 
cuenta. Es impMtante mencionar también la sensibilidad del intemptor diferencial tiene 
una tolerancia de fabricación, La misma es Esto significa que para un hterruptor 
diferencial de sensibilidad W•30m.4, algunos comenzarán a disparar con corrientes de fuga a 
partir de los 15mA mientras que todos habrán disparado con corrientes de fuga de 30mA. 
Ejercicio: Estamos en edificio de pisos, con depanamentos pisa ¿Por qué no 
único difemnaol de 30 ma en la de pwa todo el 
Hay dos Causas; 
Lo ada todo el 
qwdo Sin eléctrico, 
wg debido a la longitud de cable distribu%, fuga de cables hoce que el 
dispare. 
Fin del Ejercicio. 
Tenemos aparatos que están destinados a redes eléctricas de Corriente Continua, mientras que 
Otros están destinados para redes eléctricas de corriente alterna, V finalmente Otros pueden 
operar en los dos tipos de redes indistintamente. 
estos aparatos pueden incluir Sistemas de ajustes de umbrales de disparo 
recomendable en ámbitos domésticos), motorizaciones para implementar sistemas de cierre V 
apertura en forma remota, pantallas para mostrar los valores medidos, sistemas de 
comunicación para centralizar las mediciones en un punto común y eventualmente para 
el cierre o la voluntaria en de utraibilidad para 
facilitar el mantenimiento, etc. En general, cada una de estas opciones adicionales está 
asociado a un cierto costo adicional. 
Contacto directo 
Tenernos situaciones de "contacto directo" cuando entramos en Contacto Con conductores 
energizados desnudos. Para evitar estas situaciones, disponemos de tres procedimientos 
básicos: 
Alejamiento: Disponer las partes energizadas a suficiente distancia. Por ejemplo, en 
altura. 
Separación: Disponer Obstáculos que eviten el Contacto Con las partes energizadas. Por 
ejemplo, cerco perimetral. 
Ing. Pablo Ciappa ELECTROTECNIA -CONCEPTOS BÁSICOS DE CIRCUITOS vl.7 Eiemicjo,' E' e/ siguiente E es 220V, R2 y 
RB a 220'm RHI R_H2 a y que Rn 5&hm, que Rt2 
toma despreciable para simp-bTicar los resolver el circuito y 
indicadas en el 
del Ejercicio. 
Eierckío: En el bs mbks de y 
del Ejercicio. 
Como va hemos mencionado, el primer circuito nos tiene que Remitir 
encontrar todas las Corrientes que planteamos en el esquema original. El proceso de 
simplificación posterior no tiene por qué cumplir este requisito, pero el primer circuito si o si 
tiene cumplirlo. 
Vemos que cada Contacto directo que Se produzca dentro de la zona protegida por un 
interruptor diferencial produce el disparo de es interruptor diferencial en particular, y no el de 
otro circuito Esto es lo que el CMItacto directo 
Con el directo 1 no podemos contar con la diferencial, pero estos Casos 
corresponden a la parte que corresponde a la empresa de distribución, Con la que 
necesitamos tener ninguna posibilidad de contacto directo, 
Con este tipo de conexiones, no necesitamos el monitor permanente de aislamiento, y de 
instalarlo, ya que daría señal de a que 
intencionalmente Vinculamos el circuito a tierra. 
Ejercicio: un 
um himpam de neón 
Su de 
cebmja de 120V ad—te, 
que de SCW,iCiO CS de 90V. 
Dich a 
O, 4mA 'a 
IJ-I de la de 
Fin del 
de 'o Oibujms el electria de' 
de h— de detum'— la 
que debernos agregar en serie para que funcione adecuadamente a 2ZOV, tensión el cuerpo 
Ing. Pablo Ciappa ELECTROTECNIA -CONCEPTOS BÁSICOS DE CIRCUITOS vl.7 Si bien resulta preferible gue el circuito que se parezca en las formas con el esquema 
o bliqotvio, I o si debe es 
Fin del 
Ejercicio: Rt de SOotm RL+ y Rt • RC• y RC- de 020tvn„ Rd de RH de 
y R r de 'ndia r debuía el 'a 
de' tmmo de detem'iw e indicw si 'o Rd 
Fin del Ejercicio. 
Debido al fallo de a islamiento, la persona pasa a formar parte del circuito V puede sufrir 
lesiones graves, Pero en esta situación, mientras la persona entre en Contacto Con la 
estructura metálica que protege al cable, no se produce la corriente a tierra. 
Puesta a a y Conductor PE de protección contra Contactos indirectos 
Si bien no *'demos impedir que las fallos de aislamiento sucedan, Si podemos intentar que la 
corriente de defecto circule hacia tierra por un camino que evite al ser vio Esto se hace 
conectando a tiema la estmctura metálica de protección mecánica. A cada de estas 
coberturas metálicas de protección que conectamos a tierra la denominamos "masa". El 
conductor que usamos para esta aplicación es obligatoriarnente el de Vaina verde amarilla, V Se 
denomina "conductor de protección", El electrodo que vincula las masas con la tierra se 
denomina "Electrodo de Puesta a tie"a protección". El concepto de conectar las masas a 
tie"a directamente a tierra se aplica tanto es sistemas aislados, como en sistemas no a islados_ 
Noternos la Simbología asociada a los conductores L (Línea), N (Neutro) PE ("Protection 
Earth" — Tierra de protección), Si no ponemos las siglas, ponemos unas barras inclinadas. En el 
Caso del conductM de sólo la En el del de Nu_'tro, 
con un de color negro. En el del de 
Protección, la barra queda coronada Con Otra más Corta paralela al conductor, que Se parece a 
una letra T, 
Conectamos a tierra los caños que Contienen los conductores fijos de la eléctrica_ 
Este criterio Se hace extensivo a todos los aparatos que conectemos a la red Con carcaza 
metálica. De esto se desprende porqué los tomacorrientes tienen tres orificios: para asegurar 
que las carcasas de los aparatos que conectemos a la red también queden conectadas a tierra 
por de segwidad_ 
En el síg esq— h— a la de 
el circuito eléctrico correspondiente. 
Ing. Pablo Ciappa ELECTROTECNIA 
- CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7 E' e'éctria al e' : 
Fin del 
Ejercicio: Cemsidenamdo despreciables los de R' RC+, RC., APE V R toman do 
siguientes Rj (o RAJ y RB de 1017, RI de 44 RH de Rd de 52, Ab n, 
comente del r, la de carga, la de defecto V la que circulo persona 
e/ 220V. qué si 'a Rd 
comente de carga sale de aplicar la ley de 
E ZZOV 
comente de defecto también sale de aplkar la ley de 
220V 
= 3,03A 
1 ooon Ion 
R d + 52,706n 
corriente del generador es de 8, OSA Esta sale de aplicar la ley de k"chho" de 
Ja por persona de aplicar de 
= 3,03A 
(1000 10)n 
Es que, comente de defecto de 3, OSA recién estamos llegando a los 
Ser 
qué re"ida la miente el h — en este Si ob. el esto se 
debe a que la la Corriente la resistencia RA en Jugar de por 
Si la de defMo min más la de def«to amo asá 
también el Ser humano. Obligatoria Ja de' Circuito, 
mn del 
En e' y Rd a 21,SOgohm 
de defecto td y que circula por persona 'h, y Su tensión de CCVttOCtO oc, Sucede sc 
de defMo 
—idas: 
Rn 21.S09n4 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7 RH R, 
tensión de contacto es: 
Rn 4 
1000n Sn 
En este nuevo caso, si se reduce resistencia de defecto, nuevamente comente de defecto se 
cm "i tmbién e/ viw tmbjen y la de 
hn del 
De los dos últimos ejercicios, concluimos que incluso para un mismo valor de corriente 
atravesando el cuerpo del ser vivo de 30mA, a menor valor de resistencia de la puesta a 
tie"a de protección RA la corriente de defecto de aislamiento máxima ldmax puede tomar 
distintos valores. 
e' Z4•50'm te — de 
de torwde e' e' 
y e' r" de 
de a la o 
En e' e' de' de e' a' y 
TES 
El hs e' dibuÊdo e' 
"d y So de Id e' 
fuga a su y 
de e' 
(1000 
de "ega a JA Ja de la 
de a u, es el por que 
de p. te a 
de Contacto V tensión de seguridad UL 
El valM de impliar una persona depende de muchos 
factores, incluyendo a la persona (sus umbrales de peligro), de la resistencia de la persona, V 
hasta del momento del dia en que estemos hablando. 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7 Además, muchas de las fallas de aislamiento 
que producen Contacto indirecto, aparecen 
cuando la persona aún no entró en contacto con 
las carcasas. Por Io tanto. no podemos calcular 
la ccwiente que atravesará a la si la 
misma aún no forma parte del circuito. 
Para verificar si todas las personas están 
protegidas contra un contacto indirecto, 
entonces determinaremos la tensión a la que 
puede llegar a quedar sometida si entra en 
contacto indirecto con el circuito. A esta tensión 
la llamaremos "tensión de LJc. Esta 
i.•iiillliNNüiiiI 
tensión de contacto deberá Ser menor que el máximo valor de tensión que soportan las 
personas, y que llamamos "tensión limite de seguridad" ut. Si la persona resulta con una 
tensión de contacto mayor que la tensión limite de seguridad, deberemos tener disparo 
automático del interruptor diferencial auwnático_ El gráfico anterior muestra los valores de la 
tensión limite de seguridad. Estos valores de tensión limite dependen del tiempo. 
A nivel internacional, los valores de tensiones límites de seguridad permanentes son: 
IJL SOV para ambientes Secos, 
UL 25V para ambientes húmedos. 
LIL 12V para ambientes mojados. 
En Argentina, la ley de Higiene V Seguridad es más especificando: 
LIL 24V para ambientes Secos húmedos. 
UL 12V para 
Noternos que Con una resistencia de una tensión de Contacto en un ambiente seco o 
húmedo produce una corriente de 24rnA. ES decir que la ley de Higiene y Seguridad Laborales 
más exigente aún. 
En atinente a Ir"talaciOneS Eléctricas, la ley de Higiene y Seguridad Laboral indica que todos 
los relativos a las debe conwltar la de 
Instalaciones Eléctricas Vigente, emitida por la Asociación Electrotécnica Argentina. 
Esto trae aparejado Otra ventaja: LOS Circuitos a estudiar resultarán sencillos, porque 
a la RH y todo lo que está en "rie en el 
compromiso de determinar el valor de uc cuando hayamos calculado las corrientes. 
La tensión de Contacto a la que Va a quedar sometida persona 
ve < Raid 
En otras palabras, aplicar la expresión exacta RH o podemos 
aplicar una expresión "pesimista" RA Id. para cornpararcon de la 
tensión límite de seguridad UL 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7 Eierck'o: Estim de a —t'da Ja —do 
produce la falla indirecto) en e' circuito antero' V tenemos en instalación un interruptor 
"tomátim de m-sibilidad a BA. 
En el Ja —tida de 
C— Z V, lo voteg'da. 
Fin de' Ejercicio, 
De hecho, la vigente de la Electrotécnica Argentina es más exigente 
aún, par que indica expresamente que la sensibilidad del interruptor diferencial automático 
para proteger a las personas contra contacto indirecto es: 
< Ue /2RA 
Es decir que considera un factor de seguridad igual a 2. 
Ejercicio: El nte e' esq. Ja AEA 
7• 771 En hay falla de 
ubicar el toroide de' interruptor 
Remcw hs de hs de m-vicio, y de Io fana a 
dibu@el a 
indicado más obo@ 
Indico r que comentes mide el 'n temptor diferencial automático, 
Finalmente, en base a los simplificar el circuito, y detemnar Ja corriente de defecto y tensión 
de co 
de cwga: 
Resiste nCia de la red: 
de Cado de los cables que tengamos que considerar: 
Resistencias de puesta a de servicio y de proteccón: 
de la p m•w_• 
Resistencia de Oohm, 
Para Circuito adoptar C riteriO para cada resistencia; 
Considerarla Si en Serie tenemos Otra 50 Su 
ab i Mo s' en atm un 2% de 
El esquema can las Corrientes el te; 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7 En y e' violeta s de 
En está indicada comente de defecto que circula pot 'a puesta a de protección 
Ve m s e' lo las y 
Si e' en 
el esquema o 
Luego de simplificar circuito, nos guedaró lo te; 
Ing. Pablo Ciappa ELECTROTECNIA -CONCEPTOS BÁSICOS DE CIRCUITOS vl.7 resolución numérica queda a cargo del lector, 
Fin de' 
El neutro como protección contra los contactos indirectos 
Ya vimos que, como medida de protección contra los contactos indirectos, tenemos 
conectar a tierra todas las carcasas metálicas de los aparatos que utilicemos. Y también Vimos 
que el conductor de neutro está conectado a tierra en alguna parte del sistema. Cabe 
preguntarse si no podríamos usar al neutro como conductor de protección contra contactos 
indirectos. una primera conclusión es que este desechado en sistemas 
aislados. 
Ejercicio: El el esq. TNC q Io de 
AEA 90364-7-771, En esqum hay fallo de a's/om'knto_ 
Ubicw el de' 
Remarcar los de las comentes de y de fana a la carcasa 
luego dib el circuito eléctrico asociado, asignarles a los componentes según lo 
indicado mas Oban 
India r que mide el 
Finalmente, base a simplificw el circwto. y Ja Corriente de defecto la tensión 
de 
de cwga: 
de red: 
de cada de los cables que que considerar: 
de o de y 50hm 
Resistencia de penana; 
Resistencia de defecto; Oohm, 
Para el el 
Considerarla Si en Serie tenemos Otra 50 Su 
Considerarla Si en paralelo Otra menor que de so 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7 El esq. el te: 
En celeste y e' violeta los caminos que siguen las comentes de servicio normal. 
En de def«to e' de 
que esta cotriente de defecto pasa e' toroide entrando V pot que no produce 
de' Ote m otiw. 5i5tem 
indirectos. prohibido de 
Electrotécnica Argentima de Eléctricas en Ofkinas V 'oca les 90364.7. 
El circuito que nos queda es el 
Si e' en 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7 de e' 
asa 
Lo a cwgo 
Fin de' Ejercicio, 
Aparatos Con doble aislamiento eléctrico 
De hecho. también queda claro que los aparatos que tienen doble capa de aislamiento externo 
no requieren de la conexión a tiera Pero sólo debemos usarla si las capas mencionadas no 
ni gun signo de deterioro. El método para dentificar los aparatosque tienen doble 
presentan n 
aislamiento es el símbolo de los dos cuadrados concéntricos: 
del de protecdón 
Las de la AEA sobre la resistencia de a tierra de protección 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7 Volviendo al cable de 1,5mm' que presentamos antes. Si vamos a alimentar un calefactor 
eléctrico de 1500W, este calefactor en 220V consume una corriente de S,8A ( ISOO%V/220V)_ 
Por IO tanto, en primera instancia, podríamos suponer que podemos alimentar dos de estos 
calefactores ya que juntos, conectados en paralelo. tendremos 13,6A, que es una cantidad 
menor que los ISA que admite el cable sin calentarse excesivamente más allá de la 
admisible. Si ponemos tres calefactores simultáneos en paralelo, el quedará 
sometido a una corriente total de 20,4A, valor que resulta claramente superior a la corriente 
admisible de 15.5A. De representa 1,32 veces la corriente nominal. En este caso, se 
trata de una sobrecarga voluntaria a la cual estamos sometiendo al cable solamente, e 
pon sable, 
Siguiendo con el cable de 1,5mm2 que presentarms antes, pero con otro tipo de carga. Si 
vamos a alimentar un motor monofásico de potencia nominal 1,5kW cuando Io alimentamos 
con 220V V SOHz, decir que toma aproximadamente IOA nominales, Con este cable 
de 1,Smm2 podernos alimentar un solo motor de estos que, Si conectáramos un segunda 
motor, superaríamos los 15,5Aque admite el cable en forma permanente. Encaso de 
arranque la corriente puede ser 7,5veces más grande (valor estimado), o de 75A. Esto también 
sucede si la carga o el rotor ser bloquean sin rotar, la comente pasaría a ser 
7 ,Sveces más grande (valor estimado). es decir, 7SA. Claramente Sólo estamos conectando un 
único motor, pero por este inconveniente de origen mecánico, estamos sometiendo al motor y 
al cable a una sobreexigencia. 
La sobrecarga del cable por exceso de calefactores conectados es que, Si llega a ocurrir, es 
poco probable que nos demos cuenta de Io que estamos haciendo (sobre todo si ya hay un 
calefactor conectado, y uno conecta su propio calefactor, mientras que otra persona conecta 
el suyo pero que simultáneamenteL En ese caso, la protección 
Contra sobrecargas que debemos debería actuar bastante rápidarnente para no 
comprcwneter el cable Con que alimentamos las cargas. 
Cuando tenernos un motor que acabamos de Conectar, sabemos que este una 
corriente de que es bastante mavor a la norninal (En los ejemplos que venimos 
Viendo es veces), En el siguiente gráfico, mostramos como es la evolución temporal de la 
corriente de un motor en funcionamiento normal (azul) y en distintas condiciones que 
podemos considerar de fana (en rojo): 
Vemos que en funcionamiento normal inmensa mayoría de las veces), transcurridos unos 
segundos, la corriente vuelve a valores normales. 
Tenemos tres casos de falla por sobrecarga: 
Arranque excesivarnente largo ("prolongado" en la palabra que Se suele usar). 
Bloqueo mecánico del eje del motor, ya desde el arranque, 
o en algún momento durante el funcionamiento. 
Ing. Pablo Ciappa ELECTROTECNIA -CONCEPTOS BÁSICOS DE CIRCUITOS vl.7 El calentamiento debido a la corriente se debe al efecto Joule. y sabemos que: 
A intensidad de Corriente, tendremos mayor calentamiento, 
El calentamiento no es instantáneo, sino que lleva un cierto tiempo, 
Cuanto es la corriente, más rápidamente llegaremos a la temperatura limite 
admisible de los materiales. 
Poderes de corte 
Por IO tanto, para esta última podemos considerar los poderes de Corte último o de servicio 
El poder de Corte último es la máxima corriente que el interruptor puede interrurnpir 
los polos V extinguir el arco subsiguiente), dos Veces consecutivas Con un intervalo de 3 
minutos entre ellas. Es posible que después de la segunda apertura en esas condiciones. sea 
necesario reemplazar el aparato. 
El poder de Corte de servicio 'cs es la máxima corriente que el interruptor puede interrumpir, 
tres veces consecutivas con un intervalo de 3 minutos entre ellas. 
Luego de las tres aperturas, el intewuptor debe conducir su comente nominal, aunque 
haya perdido su poder de corte _ 
Si hubo tres aperturas Con corriente de cortocircuito, podemos concluir que la falla no es 
transitoria. 
Por Io tanto, debemos buscarla, encontrarla, y repararla. 
A continuación, cerrar el aparato sobre un circuito sano, priorizando la continuidad 
de servicio, 
Mientras buscamos un interruptor automático de repuesto y esperamos en momento menos 
perjudicial para reemplazarlo, 
Las reglamenta•tiones de eléctricas suelen exigir que los poderes de Corte último 
Icu deben ser mapres que las corrientes de cortocircuito en los puntos de la instalación donde 
Algunas ingenierías, usan el poder de Corte de Servicio para la misma En 
resultan en instalaciones de mayor COStO. Pero a la larga, tienen mayor continuidad de servicio. 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7 、 4 》 50 辷 n し D 3050 ソ 578 50 に 3 ) NO し ー 2 凵 310 』 313 edd 物 0 0- 鵞 d 上 
「 っ て 一 宿 つ 一 " 9 
っ 〕 1 
一 ま 
507 」 。 一 LOS sistemas de de energía eléctrica 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS VI. 7 Ing. Pablo Ciappa ELECTROTECNIA -CONCEPTOS BÁSICOS DE CIRCUITOS vl.7 C 【 > 50 3050U 一 S78 501d3 NOD • 之 3 081 313 Olqe-d Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS w1.7 que, si son focalizados, pueden llegar a producir carbonizaciones de materiales aislantes, es 
decir que se vuelven conductores; y por IO tanto teMremos también cortocircuitos e 
incendios. 
Mostramos que los cables tienen sección diferente según el lugar de la instalación donde Se 
encuentren. Las secciones transversales de los cables están relacionadas con los valores límites 
de corriente en los diferentes componentes de una instalación eléctrica. Estos valores límites 
están a los fenómenos de calentamiento de los conductores, 
Para que esto no suceda, las temperaturas de trabajo de diferentes partes de la instalación 
tienen que permanecer por debajo del valor máximo de cada material aislante, Para 
simplificar, supongamos que en nuestra instalación terrmos un único tipo de material 
aislante. 
Para mayores valores de corriente, mayor va a serla temperatura final que alcanza un aparato 
o cable También es importante destacar que, si se eleva la temperatura ambiente, también 
subirán valores de temperaturas alcanzadas los de la instalación 
eléctrica, Eso por ese motivo que, en el siguiente gráfico. en lugar de representar la 
T, representamos el salto tém'ico Cuando la temperatura del aparato es la 
misma que la del ambiente, el salto térmico es cero, es el punto desde donde arrancan todas 
las curvas de calentamiento en función del tiempo cuando los aparatos están fríos: 
Una cuestión que tenemos que ver es qué significa salto térmico admisible Representa 
el "Ito entre la adrnite el plástico aislante del 
cable, V la temperatura ambiente, Esto implica es que, para cada temperatura ambiente, existe 
un máximo salto térmico admisible, 
por otro lado, del análisis del gráfico se desprende que existen valores de corriente que el 
cable admite por indefinido 
La corriente admisible del cable es entonces: (En este caso). En general, la designamos como 
Toda corriente que supere si se deja superar el tiempo suficiente, es destructiva, por 10 que 
Se debe interrumpir. ¿En Cuánto debemos interrM-npirla? Antes de t', para la Corriente 
antes de para la corriente Vemos que, para mayores valores de corriente, debemos 
actuar más rápido. 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS w1.7 Si hacernos el Siguiente como IO único que limita la corriente 
que entrega la batería son las resistencias de los alambres, tendremos un 
gran valor de corriente. Pero que notaremos es que, salvo alguna 
situación muy particular, sÉmpre se temina fundiendo el alambre de 
menos sección, Esto nos lleva a concebir la primitiva protección contra 
sobrecorrientes, que es el fusi*e. 
por obvias razones, el alambre más fino no tener una funda plástica entonces_ Las 
primeras cápsulas para evitar que el metal fundido salga proyectado. eran de ¿Con 
qué criterio deberiamos seleccionar un fusible? Se debe fundir (e interrumpir el circuito) el 
alambre fusible que mencionamos antes que se ablanden los plásticos aislantes de hs otros 
cables. Esto se consigue con un alambre (En general) bastante más que el cable, 
FINO EGO 
nvo COR ro 
Pero entonces surge la pregunta. 
¿Cómo es que un alambre más fino 
que el cable admite casi la misma 
corriente? (En condiciones normales) 
La respuesta es muy sencilla: Porque 
al ser cono, disipa en forma 
constante la mayor parte del calor 
por Sus hacia los Otros 
cables más gruesos a los que está 
conectado (Esto quiere decir que la 
estructura está a esfuerzos 
térmicos algo complejos), 
Otro detalle a tener en cuenta es que 
el fusible no tiene una única curva. 
Tiene una curva que indica el inicio 
de la fusión (LO que podriarnos de sin retomo). una vez 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS w1.7 ('rigin al 
de s 
ACR 
El aumento de la distancia s, permite alejar los puntos calientes, haciendo que el fusible sea 
más lento para las sobrecorrientes moderadas, Con la disminución de e, conseguimos que las 
sobreco«ientes elevadas sean cortadas más rápidamente. 
Existen dos tipos básicos de fusibles: 
Los que protegen tanto cortocircuitos (sobrecorrientes elevadas) como sobrecargas 
(sobrecorrientes moderadas), tipo g (General), 
Los que protegen cortocircuitos (sobrecorrientes elevadas), tipo a (Acompañamiento). Por 
IO tanto, estos necesitan un dispositivo adicional para que proteja contra las sobrecargas 
(sobrecorrientes moderadas). 
En resumen: un fusible es un alambre corto que, en su calentamiento adiabático, se funde y 
luego apaga el arco, antes que el cable en su propio calentamiento adiabático aEiande o 
comprometa al plástico aislante. 
En primera instancia, debernos elegir los conductores para que sean capaces de conducir la 
corriente que los atravesará sin calentarse excesivamente. Una corriente excesiva los calentará 
por amiba de su de acMtando su vida útil. sobre este tema, 
en breve Cuando tratemos la Cuestión especlTica de las fugas en los cables. 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS w1.7 Para asegurarnos que el interruptor protege contra sobrecargas al cable, debemos verificar 
además que: 
12 SI.4S/z 
También, verificar que el dispositivo protege al cable contra cortocircuitos. En ese 
Ca so, debemos comprobar que: 
S kcs? 
Expresiones que ponemos sólo a modo de referencia, va que corresponden a temas que se ven 
en Instalaciones Eléctricas, 
Ing. Pablo Ciappa 
ELECTROTECNIA - CONCEPTOS BÁSICOS DE CIRCUITOS w1.7

 

Guía Circuitos (Corta)

Monday, April 4, 2022

8:05 AM

 

<<Electrotecnia 1.0 Teoremas.pdf.pdf>>

ELECTROTECNIA 
Teoremas y Métodos de resolución de circuitos 
Ing. Pablo Ciappa 
Int ión 
Resobaer un circuito significa averiguar qué es Io que sucede en el mismo, o conocer todas las 
tensiones V corrientes de cada uno de Sus componentes. Por IO tanto, Si tenemos r componentes, en 
primera instancia imcOgnitas_ Estas son cada una de las r ccwientes y cada una de las r 
tensiones. Así, necesitariamos 2r ecuaciones con 2r incógnitas para resohverlo. 
Si esta la situación final, un Circuito Con componentes en serie, sería algo cornp'icado de 
resolver debido a que necesitaríamos S ecuaciones con S incógnitas para conocer qué es lo que 
sucede. Sin embargo, sabemos que, si bien es cierto que tenemos 6 hcOgnitas, lo terminamos 
resolviendo con una ecuación. Veamos el siguiente ejemplo: 
Tenemos 6 incógnitas que son: E, I', U", I", Um, e Sin embargo, desde el momento que los 
están conectados en serie, decir que las tres corrientes Son iguales. V por IO 
tanto nuestm núme") de incógnitas se reduce a 4: E, Un, e Al estar conectados en serie, las 
tensiones también están relacionadas de forma tal que la fem de la fuente es igual a la suma de las 
caidas de tensión en las dos resistencias. 
E (JAI + UR2 
Por Io tanto, si sabemos dos de enas, la tercera no puede tomar cualquier valor. Esto hace que el 
número de incógnitas Se reduzca a tres. 
Si además consideramos la lev de 
Esto significa que, si conocemos la corriente, podemos averiguar las caidas de tensión en las 
resistencias, y esto reduce el número de incógnitas a una sola: La corriente/, En realidad, podría Ser 
Otra, pero usualmunte plantearemos a las cmo irrógnitas 
Para averiguarla, usamos las propiedades que mencionamos antes: 
E E R + R--,/R-2 E = R / 
En realidad, Cuando nos encontramos Con un Circuito Serie, no detenemos a hacer todo este 
análisis. Simplemente escribimos la última expresión, y reemplazamos valores en la misma 
obteniendo el valor de la corriente, 
Sin embargo, existen Circuitos más elaborados donde no es posible escribir una expresión corno la 
última, reemplazar valores y Obtener el valor de la En general, planteamos varias 
ecuaciones simultáneas, con varias incógnitas, Y al resolver dichos sistemas, obtenemos las 
corrientes. El siguiente es un ejemplo de estos casos: 
1 Ing. Pa Cía ppa 
Electrotecnia — Teoremas 1 _O En este caso, tenemos 5 elementos y por Io tanto, IO incógnitas. Al estar en serie cada uno de los 
generadores de tensión con una resistencia, Sus CorrQnteS Son iguales, restricción que reduce las 
incógnitas a 8. Como las tensiones son datos, se reducen las incógnitas a En las tres 
resistencias, si sabemos las corrientes inmediatamente averiguar las tensiones, tenemos 
otras restricciones que reducen las incógnitas a tres. si obtenemos los valores de dos de las 
corrientes, la tercera no puede tomar cualquier valor, V es Otra restricción, Asi Se reduce el número 
real de incógnitas a dos, plantear un sistema de dos ecuaciones con dos incógnitas y al 
resolverlo, podríamos saber Io que sucede en todo el circuito, 
Este análisis que acabamos de hacer no nos dice todavia cuáles son las ecuaciones que debemos 
plantear_ de los Objetivos de este capítulo es presentar el método para saber cuántas incógnitas 
tenemos realmente en circuito. El otro objetivo es presentar para plantear las 
ecuaciones necesarias para resolver los circuitos y resolverlos. Para averiguar cuál es el número real 
de incógnitas. debemos presentar las restricciones que los las restricciones 
que imponen las conexiones. 
Restricciones que imponen los 
Formalicemos los tipos de restricciones que imponen los componentes. 
una de las ellas, es la ley de en las Para una resistencia de 
20hm, al aplicarle 2 volt, circulará una corriente de IA Si duplicamos la 
tensión. la corriente también Se duplicará, La curva característica es una recta 
que pasa por el origen de coordenadas. La restricción toma la forma: 
= Rx/x 
Un generador ideal de tensión E, impone una tensión entre sus terminales, 
independientemente de la que lo Un ideal de 
tensión no puede trabajar con un cortocircuito en sus terminales, Implicaría 
tensión nula, o una contradicción. Si una pila recargable indica Su 
curva característica idealizada tiene que reflejar este comportamiento. 
Un generador ideal de corriente I, impone el val•or de la corriente que atraviesa, 
independienternente de la tensión que tenga en Sus terminales. 
NO puede trabajar en condición de circuito abierto en Sus implicaria 
corriente nula, causando una contradicción. 
Si una celda fotoeléctrica iluminada Con IO(XJW/m2 tiene una 
Corriente de Su Curva característica idealizada tiene que 
reflejar este comportamiento, Esta es la Curva "ideal" En la realidad, 
deberemos hacer algunas modificaciones para considerar que hay limites 
en la corriente que puede entregar la Célula _ 
2 
Ing. pablo Ciappa 
E I ectrotecnia — Teoremas 1 _O

 

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EierciOo Sumar m, dos primeras ecuaciones de obtenidas en el ejercicio Indicar a 
que es igual el resultado, 
Ejercicio En el siguiente grafo identificar y las magas, las ramas que los 
Eiercicio '4: Definir tensiones dei circuito y plantear las para e,' 
Plantear jas 'eyes de de las manas, y luego las cotrespondientes a los lazos. 
resultado ob ten erm» si dos expresiones obtenidas desde Jas mallas * 
¿Son linealmente imiepemj,vntes expresiones de 'a obtenidas de un circuito? 
¿Cuántas ecuaciones de KT linealmente 9'dependientes '»demos plantear circuito ? 
¿Cuál es el número de manas m de un con r y n nodos? 
Horarias = A n t/horor/as 
ll 
E I ectrotecnia — Teoremas 1 _O 
6 
Ing. pablo Ciappa Método de las corrientes de manas o de 
Es uno de los métodos sistemáticos que permiten plantear las ecuaciones necesarias por 
simple y resolver circuitos, 
Eiercicio En el te circuito detemninar las faltantes. "ego, determinar los balances de 
comentes ne tas cortadas por las lineas finas ( Ver ejemplo en el mismo circuito). 
Neto: 
¿Que 
En e' esquem de derecha indicar las corrientes de mana del circuito anterior. 
Conociendo la corriente de malla y la corriente de malla averiguamos la corriente de rama 
Cia 
18: Defmir de del ciruito, definir hs de 
r de de de 
E I ectrotecnia — Teoremas 1 _O 
Plan hs de Kirchhoff de 
de las de' 
hs de r. r 
Reordenar expresiones en función de las Corrientes 
de m 
Observando las expresiones Ob ten'das; ¿ NO tamos 
algu a manera de las mismas por inspección 
directa de' Circuito 
e Cómo definimos fem de mana? 
Sucede Si una maga tenemos varios 
R, 
generadores de ten sida ? 
¿ Cómo definimos resistencia propia de malla? 
¿ Cdtno definimos resistencia mutua entre 
7 Ing. Pa Cía ppa

 

 

 

Proporcional ida d 
Vamos a ver presentar este método por medio de un ejempb. 
E I ectrotecnia — Teoremas 1 _O 
Resolver el siguiente circuito. 
R, 
600 R, 
Normalmente averiguamos los valores de las resistencias equivalentes. Para las resistencias R' y R.: 
+ R2 2011 + bon gon 
Para las resistencias R" Rn: 
para las resistencias R. y Rn': 
podemos resolver el circuito: 
80n + aon 
+R 3 —1012+40n=50n 
E 
2001' 
¯ son ¯ 
Y ahora podernos determinar las tensiones y corrientes: 
mn 
200 
20V 
nav 
una alternativa seria preguntarnos qué generador poner para que por la resistencia de 
600Circule una corriente de La secuencia de Cálculo es la siguiente: 
1001' 
20'2 
60'2 R, 
A la derecha escribirnos el proceso de Cálculo. Vemos que Con IWV en la entrada, Obtenemos IA en 
la resistencia de Coma el real es de esto Significa que todas las tensiones y 
Corrientes deben multiplicarse por dos. 
LOS Cálculos de tensiones y corrientes en ambos casos Son sirnilares. La diferencia está en que Con el 
segundo método evitarnos todos los Cálculos de las resistencias que, Si bien no Son difíciles, 
cierto trabajo. 
de 
I I Ing. Pa Cía ppa

 

 

Ampliamente utilizado en la fisica, la única limitación que tiene es que solamente Se aplica a 
sistemas lineales, Si tenemos un circuito cualquiera con generadores de tensión y de corriente para 
el cual planteamos las ecuaciones de mallas: 
para determinar una corriente cualquiera, por ejemplo, la primera: 
Cuando desarrollamos el determinante de arriba por menores complementarios: 
+ R 22 
E I ectrotecnia — Teoremas 1 _O 
detR 
Ez +R22 
det R 
E2 +R22 
detR 
- R2K 
Así, decir que la comente de malla I depende de cada uno de los generadores tensión 
por separado. Sin embargo, esta no es la forma en que aplicamos este método. Veamos un ejemplo. 
Resolver el siguiente circuito por el principio de superposkión. 
Aplicar el principio de superposición, implica resolver el circuito analizando el efecto de cada 
generador por separado, V luego superponer los resultados parciales para Ver el resultado final. Para 
ello, ta" merm y el rewltMlte A 
continuación, "pasivamos" el generador que habia quedado activo, "activamos" un generador de los 
que habían quedado "pasivados", y resolvemos el circuito resultante. Así, continuamos hasta que 
todos los del circuito actiwdOS, por IO menos y a IO una Para 
resolver el circuito, debemos primero identificar los sentidos que consideraremos positivos de todas 
las magnitudes que Vamos a calcular 
12 
Ing. pablo Ciappa Y Con estas referencias, deberíamos llenar la siguiente tabla: 
Gen. ACt. E: 
Y de esta manera averiguarnos todas las tensiones y todas las comentes de cada uno de los 
del circuito. Antes de embarcarnos en el llenado de toda la tabla, primero analicemos 
Si anticipar algunos resultados Sin tener que hacer Cálculos, V Si realmente es necesario 
completar toda la tabla para poder resolver el circuito. Veamos el caso del generador Cuando 
está activo, entrega 4", y el resultado final tiene que ser también Evidentemente tiene que 
entregar OVcuando está "pasivado". 
Gen. E: 
TOTAL av 
La única forma de asegurar esto es reemplazando al generador E! por un cortocircuito (cable) 
cuando está "pasivo" V tiene que entregar OV_ Así, cuando está activo en generador de corriente 
el circuito q'r tenemos que resolver es el siguiente: 
Así, podernos resolver el Circuito parcial: 
Y completar parcialmente la tabla: 
Gen. Act. E: 
Veamos el caso del generador L: Cuando está entrega 'AV, V el resultado final que Ser 
tamb"n IA_ Evidenternente tiene que entregar 04 cuando está "pasivadO" 
E I ectrotecnia — Teoremas 1 _O 
13 
Gen _ ACt_ 
Ing. pablo Ciappa

 

Tomemos un circuito para el cual ya conocemos Sus tensiones y corrientes. 
60vl Ion 
100 v 
En la rama de la resistencia central, que tiene y SA, intercalamos dos generadores de 60V con 
sentidos opuesto. Nos quedará la siguiente: 
60vl 
100 v 
Además de agregar las dos fuentes, ponemos un voltímetro tal como el que hemos dibujado el 
mismo indica OV_ Esto significa que entre los dos puntos no hay diferencia y IO 
tanto podemos unirlos con un cable. 
1001' 
601' 
100 
El principal indicador de que la situación es normal, es que por el cable que pusimos circulan OA. Esto 
Significa podernos eliminar los dos elementos (La y de los generadMes que 
agregamos, Y el resto del circuito Se Sigue comportando de la mSma manera como si no Se hubiera 
enterado del cambio. 
44 
100 
601'1 
Ion 
1001' 
Electrote cnia — T 
loor La resistencia involucrada en el cambio que hicimos se entera del cambio, La conclusión es 
que podemos reemplazar una resistencia del circuito por un generador de tensióm cuya tensión sea 
igual a la tensión que tiene la resistencia, V el resto del circuito Se seguirá comportando de la misma 
manera, como verificar muy f*ilmente, 
Otra posibilidad es hacer el reemplazo Con dos de corriente en antiparalelo. 
E I ectrotecnia — Teoremas 1 _O 
100V 
64 
64 
60 v 
podemos ver que hemos incorporado dos amperímetros que tienen Gracias a esto, 
podemos cortar cualquiera de los dos cables donde están los amperímetros, o los dos, sin que se 
entere el resto del circuito o la m isma resistencia involucrada. ES decir que podemos Seguir 
trabajando el siguiente circuito; 
I OOV 
¿Para qué sirve este principio que nos pide que sepamos la solución del circuito previamente? 
Observación: Aplicar el principio de sustitución, implica que el circuito antes y después de la 
sustitución tener la misma solución. 
16 
Ing. pablo Ciappa En el SigLiente Caso, determinar cuándo es posible aplicar el principio de sustitución. 
En el siguente caso, determinar si es aplicable o no el principio de 
Dado el siguiente circuito, aphcando el principio de sustitución en RU analizar las corrientes que 
circulan por cada generador. 
Ing. Pa Cia 
E I ectrotecnia — Teoremas 1 _O Teorema de o estrella -triángulo 
A veces, algunos circuitos que presentan un elevado número de ecuaciones necesarias para 
resolverlos, pueden simplificarse mediante esta transformación. Los circuitos trifásicos son algunos 
de los casos donde podemos aplicar este método. 
Determinar las lecturas de los óhmetros a uno por ves) si las resistencias R", R. y Rc 
Lectab - RA + RE 
valen l, 2 V 
Los de las lecturas serán: 
Lectbe 
Lect bc Rc 
- 2n+3n-5n 
Lectac = = In + sn 
para el esquema del caso anterior, si las lecturas dieron 7, 9 y ¿cuánto vakn las 
resistencias individuales? 
Hay varias fom.as de analizar este caso. La más intuitiva es que si las kcturas aumentaron 
idénticamente en es porque cada resistencia aumentó 212_ Sin esta respuesta requiere 
que primero resultados anteriores, que exista simple entre las 
resistencias, y cierta habilidad para los manejos de números. 
vamos a responder la pregunta desde Cero. ES decir que tenemos que resolver el Siguiente Sistema 
de ecuaciones: 
RA + — 7n 
Su solución es muy sencilla. De todos los métcMSos disponibles, podemos aplicar el de sumas y restas. 
Por ejemplo, Si sumamos las dos primeras ecuaciones V restumOS la tercera: 
+ Re) + (RA + (Rg+ Re) - 912 
2RA— R, —312 
De la misma determinaremos que: 
RE — 412 
Si las tres resistencias estuvieran dentro de una caja negra con sólo tres bornes a, b, y c accesibles, 
mediante medidas externas, podemos cómo Son los componentes. 
18 Ing. pablo Cía ppa 
E I ectrotecnia — Teoremas 1 _O

 

Para determinar la resisterxia de puesta a tierra de una jabalina (Electrodo de PAR), Se hincaron 
(entemaron parcialmente) dos jabalinas auxiliares más cortas (Electrodo Aux), según el siguiente 
E I ectrotecnia — Teoremas 1 _O 
Caja de 
inspeccion 
Las mediciones dieron: 
Rt 2sn 
R, 300 
R, asn 
Jabalina 
Deterrninar la resistencia de la puesta a tierra en cuestión, ¿ Cómo Son las otras resistencias? 
Sabiendo que la resistencia de puesta a tiewa de Lma jabalina es: 
Si la jabalina tiene una longitud de 1,5m ¿Cuánto vale la resistividad del terreno? 
19 
Ing. pablo Ciappa

 

 

Determinar las lecturas de las óhmetros (Aplicados a uno por ves) Si las resistencias R", Rgey 
+ RCA 
REARAB 
RE c + + REA 
Rea valen respectivamente 3, 67C), 110 V 5, m. 
Red/ RE) 
LOS valores de las lecturas serán: 
Le ctab 
RAO + Rec + RCA 
Rac(RA8 + R") 
Rac + RAO + 
RcA(R8c + RAO) 
+ 5,5n) 
+ 5,5n) 
1142 + 367:2 + 5,sn 
55n(11n + 3,67n) 
- s,sn + +3.67n - 
Lect ab = R"'/ REA) 
Lea bc = R"' 
— 3,0012 
11/29,17/2 
= 5,oon 
= 4,oon 
20.17n 
Podemos ver que los resultados son iguales a los obtenidos en el ejercicio anterior. Es decir, hs dos 
circuitos Se comportan exactamente de la misma manera, Si estamos en presencia de una caja negra 
con tres terminales y medimos entre ellos 3, 5 y 40: ¿Cómo podriamos saber si adentro las 
resistencias están en estrella o en triángulo? NO podriamos, al menos que la abramos para Ver qué 
hay adentru Esto se a que los dos circuitos son equivalentes. Esta equivalencia se 
el teorema de Kennelly que es el tema del próximo ejercicio. 
Igualando las expresiones de los ejerCiCOS I y 4, despejar los valores de las resistencias de la estrella 
en función de las resistencias del triángulo. 
Le Ctab RA + RB 
Lectbc RB 
+ REA) 
Lectac RA + Rc 
RCA + Rac + RAF 
Así, sumando Lect ab con Lect ac, y restando be. 
randa que tenemos 
RAB 
común y distribuyendo: 
RMRw + RcA(Rgc + Rn) — Rec(Rag ACA) 
Y simplificando nos queda: 
2C) Ing. Pa Cia 
E I ectrotecnia — Teoremas 1 _O RAS + REC + RCA 
Así, podemos decir que: 
RAN + + 
Rgc 
Y de esta manera, tenemos las expresiones de las resistencias en estrella. 
las resistencias del triángub en de las resistencias de la estrella. 
Si llamamos 
RT RAS + Rac + 
Entonces las últimas expresiones anteriores son: 
Rgc 
Si multiplicamos estas expresiones mam de a dos sumumos, tendremos: 
R,teRcA RecR,te RecRAs R caRgc RcARge RAE REA 
RARE + + RcRA - 
Reacomodando: 
RhRacRca + RA8RicRcA + RA8REcRcA 
En el Segundo miembro, podemos Sacar factM común 
(RAS + REC + RCA) 
El paréntesis es igual a RE 
RAsRgcRcA 
RARO + RaRc + — 
Dividiendo mam por 
NOS queda: 
RARA + RARE + RcRA 
Con IO que podemos sirnplificar: 
E I ectrotecnia — Teoremas 1 _O 
Así, podemos escribir: 
RARE + RERc + RcRA 
— Rac 
RARE + RERc + RcRA 
21 
Ing. pablo Ciappa RARO + + RcRA 
REC 
Teorema de Thevenin (también como de Von Helmholtz) 
Basándonos en el principio de sustitución y en el de superposición podemos llegar al teorema de 
Thevenin, El teorema indica que Si podernos identificar dos partes de un Circuito en donde la 
vinculación entre ambas es mediante dos cables, se puede sustituir una de las partes del 
circuito si es lineal, por un generador de tensión en serie con una resistencia. 
Supongamos, para sirnplificar, que una de las partes es una resistencia Rt que llamarernos de 
carga, Así, nos queda la siguiente situación : 
RESTO DEL 
CIRCUITO 
Es decir que, en la resistencia de carga, tendremos ccwiente que produce Ema caída de 
tensión h. Aplicando el principio de sustitución, reemplacemos la carga por un generador de 
corriente, 
RESTO DEL 
cacuro 
Aplicamos ahora el principio de superposición de la siguiente manera: Pasivamos el generador 
un lado. V después todos los generadores del RESTO DEL CIRCUITO simultáneamente. Así: 
A la izquierda vernos el Circuito Con el generador de corriente pasiwada, por IO que deÉrnos el 
circuito abierto, ta corriente es nula, pero aparece una tensión que denominamos tensión en vacio 
E", A la derecha, activamos al generador de corriente mientras que hemos pasivado todos los 
generadores que hay en el RESTO DEL CIRCUITO, Alli solo quedan resistencias. LOS generadores 
de tensión fueron reemplazados por mientras que los generadores independientes de 
corriente fueron reemplazados por circuitos abiertos, La tensión que presenta el circuito de hs 
generadores pasivados es a la corriente de carga multiplicada por la resistencia equivalente 
22 Ing. Pa Cía ppa 
E I ectrotecnia — Teoremas 1 _O

 

Cuando superponemos los resultados nos queda la Siguiente situación en el circuito Con la 
resistenci 
RESTO DEL 
CIRCE," ro 
Vemos que la tensión de s*ida es, por ley de igual a RNE, mientras que el principio de 
superposición igual a Igualando ambas expresiones:RL/L = Eo — + 
Es decir que tenemos el siguiente circuito: 
Donde definimos como: 
Tensión de Thevenin Em a E', es decir la tensión que aparece en donde estaba la carga 
cuando la desconectamos quedando un Circuito abierto. 
Resistencia de Thevenin Rm a Rm es decir la resistencia que presenta el resto del circuito 
cuando pasivamos todos sus generadores V reemplazamos a la carga óhmetro. 
Conceptualmente, IO que debemos recordar principalmente es el circuito equivalente, Sus 
definiciones (que además contienen el procedimiento para calcular las partes del circuito 
Determinar el equivalente de Thévenin usando los de los dos experimentos. 
Determinar el equivalente de Thévenin usando los de los dos experimentos. 
23 Ing. pablo Cía ppa 
E I ectrotecnia — Teoremas 1 _O Determinar el equivalente de Thévenin usando los de los dos experimentos. 
Determinar la en la resistencia Por medio del método o teorema de 
Detenninar los equivalentes de Thévenin de los siguientes circuitos. 
24 Ing. Pa Cia 
E I ectrotecnia — Teoremas 1 _O

 

 

Teorema de Morton 
Nuevamente, basándonos en el principio de sustitución y en el de podemos llegar al 
teorema de Norton_ El teorema indica que si podemos identificar dos partes de un circuito en donde 
la vinculación entre ambas es sólo mediante dos cables, se puede sustituir una de las partes del 
Circuito Si es lineal, por un generador de Corriente en paralelo Con una resistencia. 
Supongamos, para simplificar. que una de las partes es sólo una resistencia R, que llamaremos de 
carga. Así, nos queda la siguiente Situación: 
RESTO DEL 
CIRCUITO 
Es decir que en la resistencia de carga, tendremos una corriente que produce una caida de tensión 
h. Aplicando el principio de sustitución, reemplacernos la carga por un generador de tensión. 
RESTO DEL 
cacuro 
Aplicarnos ahora el principio de superposición de la siguiente manera: Pasivamos el generador Vt 
por un lado, y después generadores del RESTO DEL CIRCUITO simultáneamente. Así: 
A la izquierda vemos el circuito con el generador de tensión h pasivado, por Io que dejamos el 
cortocircuito. ta tensión es nula, pero aparece una corriente de cortocircuito que denominamos 
Corriente de Norton A la derecha, activamos al generador de tensión Ve. que hemos 
pasivado todos los que hay en el RESTO DEL CIRCUITO Alli solo quedan 
resistencias, Los generadores de tensión fueron reemplazados por cortocircuitos, mientras que los 
generadores independientes de corriente fueron reemplazados por circuitos abiertos, o Sea, Vernos 
la mima resistencia el caso del equivalente de La Comiente el Circuito de 
los generadores pasivados es igual a la tensión de carga dividida la resistencia equivalente R«, 
pero debemos considerar que está dada vuelta, 
Cuando superponemos los resultados "os queda la Siguiente Situación en el Circuito Con la 
resistenc a: 
25 Ing. pablo Cía ppa 
E I ectrotecnia — Teoremas 1 _O RESTO DEL 
CIRCE" ro 
Vemos que la corriente de salida es igual a la corriente de cortocircuito, menos %/R«. ES decir 
que tenemos el siguiente circuito: 
Pero cuando un generador de corriente entrega una corriente proporcional a la tensión en sus 
extremos, podemos reemplazarlo por una resistencia. Por Io tanto. nos quedará el siguiente circuito: 
Donde definimos como: 
Corriente de Norton a es decir la corriente que circula en donde estaba la carga cuando la 
desconectamos quedando un cortocircuito en Su lugar. 
Resistencia de Norton R v a es decir la resistencia que presenta el resto del circuito cuando 
pasivamos todos sus generadores y reemplazamos a carga por un óhmetro. 
Conceptualmente, IO que debemos recordar principalmente es el circuito equivalente, sus 
definiciones (que además contienen el procedimiento para calcular las partes del circuito 
equivalente), 
Determinar el equivalente de Norton los de dos 
E I ectrotecnia — Teoremas 1 _O 
26 
Ing. pablo Ciappa Si para averiguar la tensión de Thevenin dejábamos un circuito abierto en lugar de la resistencia de 
carga, ¿por qué no dejamos un cortocircuito para averguar la corriente de Norton directamente? 
Determinar la corriente en la resistencia R/ Por medio del rnétodo o teorema de Norton. 
Determinar los equivalentes de Norton de los siguientes circuitos. 
¿Qué conclusiones podemos sacar en este caso ? 
E I ectrotecnia — Teoremas 1 _O 
27 
Ing. pablo Ciappa

 

Teorema de máxima de potencia 
El teorema de máxima transferencia de potencia busca determinar las condiciones para obtener la 
máxima potencia en una resistencia que en general es considerada como de carga. 
R, 
La potencia que Se disipa en la resistencia de carga es: 
Rx12 R x Rx inspección directa, 
el mayor valor de potencia en R, Io tendremos cuando X. se anula. Esto Io podemos conseguir, 
insertando una reactancia de signo opuesto a la existente en serie. A veces no podemos anularla y 
debemos dejarla Como está. Este es uno de esos casos. 
La otra variable que "Iteresa estudiar es R._ Si hacemos la inversa de la 
Buscar el máximo de la es buscar el de su iwersa. Además, el de la 
última expresión no influye, por Io que si hacemos la derivada del numerador e igualando a cero: 
E I ectrotecnia — Teoremas 1 _O 
d(Rx + 2Re + (RS + X$)/Rx) 
(RS + Xe2) 
Izel 
En Si la resistencia de carga toma el valor del de la equivalente O de 
Thévenin, tendremos la máxima potencia disipada en esa misma resistencia. 
escale ra 
En el sigtúente circuito, determinar la corriente en la resistencia R' 
R, 
28 
Ing. pablo Ciappa

 

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Sunday, May 8, 2022

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Sunday, May 15, 2022

11:25 PM

 

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Guia Trifasica

Friday, August 12, 2022

3:26 PM

 

<<Electrotecnia GUIA 4 V6 Corriente Alterna Trifásica.pdf>>

 

 

Guia Correccion Cos Phi

Friday, August 12, 2022

3:31 PM

 

<<GUIA_5_Electrotecnia_Corrección de cos phi.pdf>>

 

 

Labos

domingo, 9 de marzo de 2025

00:53

 

Labo 1 - CC

Wednesday, June 22, 2022

9:13 PM

 

<<TP1.docx>><<TP1.xlsx>><<LAB01 - Practica de laboratorio N1_Rev 0.pdf>>

 

 

Labo 2 - CA

Monday, May 30, 2022

7:13 PM

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Exámenes

Friday, August 12, 2022

3:27 PM

 

1P Viejos

Sunday, May 15, 2022

11:30 PM

 

Parcial Electrotecnia - Prof. Ciappa 
1. Tomar como carga a R3. Determinar el equivalente de Thevenin e indicar el maximo valor de 
potencia que podemos obtener de ella. Datos: RI=IO ohm, 20 ohm, 60V, E2=100V. 
2. Circuito magnetico con entrehierro. Hierro permeabilidad relativa de 2000, 200 espiras, circula 
corriente de ICA. Determinar los amper espiras que tiene el entrehierro. 
3. Demostrar que el valor eficaz de una señal sinusoidal es el valor pico dividido la raiz de 2. 
4. Circuito RLC en paralelo. Te daba la corriente y te pedia calcular la corriente que circulaba entre 
el inductor y la resistencia, y dibujar el diagrama fasorial. 
El — 
R3

 

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14 
x: 
T 
2T 
Para la siguiente forma de onda que corresponde a una corriente, ¿qué sucede con el valor 
eficaz de la misma si reducimos el valor XI? 
(10/10 puntos) 
Aumenta 
Se mantiene igual 
Disminuye 
Ninguna de las opciones anteriores Correcta En un circuito ferromagnético con entrehierro y una bobina por la que circula corriente, 
¿cuáles son los resultados de decrementar el entrehierro (reducir la separación entre las piezas 
de hierro a la derecha)? 
(5/5 puntos) 
Aumentan los NI del entrehierro. 
Aumentan los NI del material ferromagnético. 
Los valores de NI del entrehierro y del material ferromagnético se mantienen sin cambios. 
Ninguna de las respuestas anteriores es correcta. ¿A qué circuito alimenta el generador de tensión si corresponde el siguiente diagrama 
fasorial? 
(5/5 puntos) 
l' Alimenta a un paralelo formado por dos circuitos serie ambos 
Alimenta a un paralelo formado por dos circuitos serie uno R—L. yel otro L—C. 
Alimenta a una serie formado por dos circuitos paralelos ambos R-L. 
Alimenta a unz serie formado por dos circuitos paralelo uno R-l— y otro L-C. 
Alimenta a un paralelo formado por dos circuitos serie ambos R.C. 
Alimenta a una serie formado por dos circuitos paralelo uno R-L. y otro L-CL 1, 
Para el siguiente circuito trifásico, ¿qué consecuencias trae la interrupción del conductor de 
neutro? + 
(5/5 puntos) 
La fase con menar impedancia pasa tener mayor tensión. 
L? fase con menor impedancia tener mayor corriente, 
Ninguna de las opc'ones anteriores es correcta. x 
La siguiente señal cuadrada tiene un ciclo de trabajo del 50%. ¿Cuáles son los resultados de 
llevar a la mitad de tiempo al periodo T? 
(0/5 puntos) 
El valor medio se incrementa. 
El valor medio se mantiene constante. 
El valor medio disminuye. 
"Incorrecto" ¿Cuáles de las siguientes afirmaciones son correctas si rellenamos el entrehierro de la columna 
central con un trozo de de material ferromagnético? * 
(5/5 puntos) 
Se incrementa el flujo de la columna izquierda, 
Se incrementa el flujo de la columna derecha. 
Se decrementa flujo magnético de la columna izquierda 
Ninguna de las opciones anteriores es correcta, Para el siguiente circuito, ¿qué cambio deberíamos hacer en el fasorial? 
(5/5 puntos) 
R2 
50 
XL2 
20 
IOf) 
IOA 
11,30 
Incrementar largo del fasor IL 
Incrementar largo del fasor IR 
Incrementar largo del fasor l. 
Incrementar el largo del fasor L]P. 
Incrementar el largo del Ésor UR. 
Incrementar largo del fasor LIL x 
z, 
12 
Para el siguiente circuito trifásico ¿cuáles de las siguientes opciones son válidas? 
(2/5 puntos) 
Al interrumpir el conductor de neutro ia corriente de neutro pasa a valer OA. 
El interrumpir el conductor de neutro la tensión de neutro pasa valer DV, 
A/ restablecer el conductor de neutro la corriente cada una de las tensiones de fase en la carga igualan 
la tensión del generador 
Ninguna las respuestas es correcta. 
"Parcialmente correcto" x 
¿Cuál de las siguientes afirmaciones es correcta? La corrección de coseno phi en una 
instalación se hace para: • 
(5/5 puntos) 
No pagar la multa por bajo Coseno phi. 
Reducir la corriente del generador. 
Reducir caída de tensión en la red. v/ 
V ' Todas las opciones anteriores son correctas, 
Ninguna de las opciones anteriores son correctas. En el siguiente esquema el imán está fijo ¿Qué sucede si tomamos dos extremos de la espira 
en diagonal y tiramos de ellos? * LT 
(5/5 puntos) 
No sucede nada. 
SE induce una fem en la espira en sentido horario (desde nuestro punto de visión). 
Se induce una fem en la espira en sentido antihorario (desde nuestro punto de visión). 
Ninguna lascpciones anteriores es correcta. 18 
En el método de medición de potencia con dos wattfmetros usado en sistemas trifásicos, 
cuales de las siguientes afirmaciones es correcta cuando los dos wattímetrõs entregan la 
misma lectura? * 
(5/5 puntos) 
Sr 
6 
La Carga es resistiva pura. 
La carga es reactiva pura. 
dos primeras opciones son correctas, 
Ninguna de las anteriores opciones son correctas. En el método de medición de potencia con dos wattfmetros usado en sistemas trifásicos, 
cuales de las siguientes afirmaciones es correcta cuando los dos wattímetros entregan la 
misma lectura? (asumimos que los instrumentos está bien conectados) * 
(5/5 puntos) 
potencia reactiva es nula. 
potencia activa es nula. 
La potencia reactiva es la suma de las lecturas de los dos wattfmetros. 
La potencia activa es 'a sum— de hs lecturas de los dos wattímetros. 
LR potencia reactiva es l; resta de las lecturas de los dos Wõttimstros. 
Opción Sl_a potencie activa resta lecturas de los dos wattjmetrõs. ¿Cuál de las siguientes se ajusta mejor la definición de bornes homólogos de dos bobinas? 
(0/5 puntos) 
Son los bornes por donde tienen que entrar las corrientes para que los flujos magnéticos se sumen. 
Son los bornes por donde tienen que entrar las corrientes para que las fuerzas magnetomotrices se sumen, 
Son los bornes por donde tienen que entrar las corrientes para que los campos magnéticos se sumen. 
Son los bornes por donde tienen que entrar las corrientes para que las intensidades de campo magnéticos 
se sumen. 
Ninguna de las opciones anteriores se ajusta a la definición de bornes homólogos. 18 
En el método de medición de potencia con dos wattímetros usado en sistemas trifásicos, 
cuales de las siguientes afirmaciones es correcta cuando los dos wattímetros entregan la 
misma lectura? * CF) 
(0/5 puntos) 
La carga es resistiva pura. 
La carga es reactiva pura. 
Las dos primeras opciones son correctas. 
Ninguna de las anteriores opciones son correctas. x 
14 
1 
¿Cuáles son los resultados de rellenar el entrehierro de la columna central con un trozo de de 
material ferromagnético? * 
(5/10 Points) 
Se incrementa el flujo de la columna izquierda. 
Se incrementa el flujo de la columna central. 
Se incrementa el flujo de la columna derecha. 
Ninguna de las opciones anteriores es correcta. 
"Parcialmente correcto" ¿A qué circuito alimenta el generador de tensión si corresponde el siguiente diagrama 
fasorial? k 
(10/10 Points) 
Pl Alimenta a un paralelo formado por dos circuitos serie ambos R-L v/ 
Alimenta a un paralelo formado por dos circuitos serie uno R-L. y el otro L-C. 
Alimenta a una serie formado por dos circuitos paralelos ambos R-L. 
Alimenta a una serie formado por dos circuitos paralelo uno R-L y el otro L-C. 
Alimenta a un paralelo formado por dos circuitos serie ambos R-C. 
Alimenta a una serie formado por dos circuitos paralelo uno R-L y el otro L-C. x 
En un circuito ferromagnético con entrehierro y una bobina por la que circula corriente, 
¿cuáles son los resultados de aumentar el entrehierro (aumentar la separación entre las piezas 
de hierro a la derecha)? * 
(0/5 Points) 
Aumentan los NI del entrehierro. v' 
Aumentan los NI del material ferromagnético. 
Los valores de NI del entrehierro y del material ferromagnético se mantienen sin cambios. 
Ninguna de las respuestas anteriores es correcta. 
"Incorrecto" 14 
¿A qué circuito alimenta el generador de tensión si corresponde el siguiente diagrama 
fasorial?* LTD 
(0/5 puntos) 
Alimenta a un paralelo formado por dos circuitos serie ambos R-L. V 
Alimenta a un paralelo formado por dos circuitos serie uno R-L y el otro L-C. 
Alimenta a una serie formado por dos circuitos paralelos ambos R-L 
Alimenta a una serie formado por dos circuitos paralelo uno R-L. y el otro L-C. 
Alimenta a un paralelo formado por dos circuitos serie ambos R-C. 
Alimenta a una serie formado por dos circuitos paralelo uno R-L. y el otro L-C. ¿Cuál de las siguientes afirmaciones es correcta? La corrección de coseno phi en una 
instalación se hace para: * CF)) 
(0/5 puntos) 
No pagar la multa por bajo coseno phi. 
Reducir la corriente de la carga. 
Reducir la corriente del generador. v/ 
Todas las opciones anteriores son correctas. 
Ninguna de las opciones anteriores son correctas. LI 
11 
u 
La siguiente señal cuadrada tiene un ciclo de trabajo del 50%. ¿Cuáles son los resultados de 
duplicar el valor pico y llevar a la mitad de tiempo al periodo T? * T) 
(5/5 puntos) 
El valor medio se incrementa. v/ 
El valor medio se mantiene constante. 
El valor medio disminuye. 
El valor eficaz aumenta v/ 
El valor eficaz se mantiene constante. 
El valor eficaz disminuye En el siguiente esquema el imán está fijo ¿Qué sucede si tomamos dos extremos de la espira 
en diagonal y tiramos de ellos? * 
(0/5 puntos) 
No sucede nada. 
Se induce una fem en la espira en sentido horario (desde nuestro punto de visión). 
Se induce una fem en la espira en sentido antihorario (desde nuestro punto de visión). 
Ninguna de las opciones anteriores es correcta. 15 
1 
Para el siguiente diagrama fasorial, ¿cuales de las afirmaciones son correctas? * CF) 
(0/5 puntos) 
El fasor rojo corresponde en un circuito RLC serie a la tensión compuesta del capacitor y de la resistencia. v/ 
El fasor rojo corresponde en un circuito RLC serie a la tensión compuesta de la inductancia y la resistencia. 
El fasor rojo corresponde en un circuito RUC serie a la tension compuesta de la inductancia y el capacitor. 
El fasor rojo corresponde en un circuito RLC paralelo a la tensión compuesta del capacitor y de la resistencia. 
El fasor rojo corresponde en un circuito RLC paralelo a la tensión compuesta de la inductancia y la 
resistencia. 
El fasor rojo corresponde en un circuito RLC paraleo a la tension compuesta de la inductancia y el capacitor. 16 
1 
En un circuito ferromagnético con entrehierro y una bobina por la que circula corriente, 
¿cuáles son los resultados de aumentar el entrehierro (aumentar la separación entre las piezas 
de hierro a la derecha)? * 
(0/5 puntos) 
Aumentan los NI del entrehierro. v/ 
Aumentan los NI del material ferromagnético. 
Los valores de NI del entrehierro y del material ferromagnético se mantienen sin cambios. 
Ninguna de las respuestas anteriores es correcta. El siguiente es el diagrama fasorial de un circuito monofásico RLC serie alimentado con un 
generador de alterna de valor eficaz de la tensión constante. Si aumentamos el valor de la 
resistencia, ¿cuáles de las siguientes afirmaciones son correctas? * 
(0/5 puntos) 
El valor eficaz de la corriente aumenta. 
El valor eficaz de la corriente disminuye. 
El valor eficaz de la tensión en la resistencia aumenta. v/ 
El valor eficaz de la tensión en la resistencia disminuye. 
Ninguna de la opciones anteriores es correcta. 12 
Material I 
Material 2 
En el circuito ferrmagnético de la figura, ¿cuáles son los resultados de incrementar la sección 
transversal del Material 2? * 
(0/5 puntos) 
El flujo magnético del Material 1 disminuye. 
El flujo magnético del Material 2 se vuelve mayor que el correspondiente al Material 1 
El flujo magnético del Material 2 se incrementa. V 
Ninguna de las opciones anteriores es correcta. 20 
¿Cuáles de los siguientes fasoriales corresponden a un circuito RLC serie donde XI es mayor 
que XC? * LTD 
(5/5 puntos) 
El fasorial A 
El fasorialB N./ 
El fasorial C 
El fasorial D 
Ninguno de los fasoriales corresponde 19 
Para el siguiente circuito trifásico balanceado, ¿cuáles de las siguientes opciones son válidas? * 
(3/5 puntos) 
Al interrumpir el conductor de neutro la corriente de neutro de un cierto valor inicial pasa a valer OA 
El interrumpir el conductor de neutro la tensión de neutro de un cierto valor inicial pasa a valer OV. 
VI Al interrumpir el conductor de neutro la corriente de neutro sigue valiendo OA 
VI El interrumpir el conductor de neutro la tensión de neutro sigue valiendo OV, v/ 
Ninguna de las respuestas es correcta, s/ 10 
¿Cuáles son los resultados de rellenar el entrehierro de la columna central con un trozo de de 
material ferromagnético? * 
(0/5 puntos) 
Se incrementa el flujo de la columna izquierda. v/ 
Se incrementa el flujo de la columna central. v/ 
Se incrementa el flujo de la columna derecha. 
Ninguna de las opciones anteriores es correcta. En el método de medición de potencia con dos wattímetros usado en sistemas trifásicos, 
cuales de las siguientes afirmaciones es correcta cuando los dos wattímetros entregan la 
misma lectura? (asumimos que los instrumentos está bien conectados) * 
(3/5 puntos) 
le La potencia reactiva es nula. s/ 
La potencia activa es nula. 
La potencia reactiva es la suma de las lecturas de los dos wattímetros. 
La potencia activa es la suma de las lecturas de los dos wattímetros. v/ 
La potencia reactiva es la resta de las lecturas de los dos wattímetros. 
Opción 6La potencia activa es la resta de las lecturas de los dos wattímetros. 11 
El módulo de una impedancia a pulsación constante formada por varios componentes, * 
(5/5 Points) 
Puede ser menor a la suma de los módulos de las reactancias que lo conforman. 
Puede ser mayor a la suma de los módulos de las reactancias y las resistencias que lo componen. 
Puede ser mayor al módulo de la resistencia que lo conforman. 
Representa un fasor o vector que rota x 
1 
Material 1 
Material 2 
En el circuito ferrmagnético de la figura, ¿cuáles son los resultados de incrementar la sección 
transversal del Material 2? * 
(0/5 Points) 
El flujo magnético del Material 1 disminuye. 
El flujo magnético del Material 2 se vuelve mayor que el correspondiente al Material 1 
El flujo magnético del Material 2 se incrementa. v/ 
V Ninguna de las opciones anteriores es correcta. 
"Incorrecto" ¿Cuál de las siguientes se ajusta mejor la definición de bornes homólogos de dos bobinas? 
(5/5 Points) 
Son los bornes por donde tienen que entrar las corrientes para que los flujos magnéticos se sumen. 
Son los bornes por donde tienen que entrar las corrientes para que las fuerzas magnetomotrices se sumen. 
Son los bornes por donde tienen que entrar las corrientes para que los campos magnéticos se sumen. 
Son los bornes por donde tienen que entrar las corrientes para que las intensidades de campo magnéticos 
C) 
se sumen. 
Ninguna de las opciones anteriores se ajusta a la definición de bornes homólogos. ¿Cuál es el resultado sobre la recta de entrehierro que trazamos sobre la curva B H del 
material ferromagnético al incrementar la separación de entrehierro en el siguiente circuito 
magnético? * 
(5/5 Points) 
50,4e/cnt 
100,4e/cm 
C) 
La recta de entrehierro aumenta su pendiente. 
La recta de entrehierro mantiene su pendiente. 
La recta de entrehierro disminuye su pendiente. v/ 
Ninguna de las opciones anteriores es correcta ¿Cuáles de los siguientes fasoriales corresponden a un circuito RLC serie donde XL es mayor 
que 
(5/5 Points) 
El fasorial A 
El fasorialB v/ 
El fasorial C 
El fasorial D 
Ninguno de los fasoriales corresponde El siguiente es el diagrama fasorial de un circuito monofásico RLC serie alimentado con un 
generador de alterna de valor eficaz de la tensión constante. Si aumentamos el valor de la 
resistencia, ¿cuáles de las siguientes afirmaciones son correctas? * CF) 
(5/5 Points) 
El valor eficaz de la corriente aumenta. 
El valor eficaz de la corriente disminuye. 
El valor eficaz de la tensión en la resistencia aumenta. v/ 
El valor eficaz de la tensión en la resistencia disminuye. 
Ninguna de la opciones anteriores es correcta. En el siguiente esquema el imán está fijo ¿Qué sucede si tomamos dos extremos de la espira 
en diagonal y tiramos de ellos? * 
(0/5 Points) 
No sucede nada. 
Se induce una fem en la espira en sentido horario (desde nuestro punto de visión). v/ 
Se induce una fem en la espira en sentido antihorario (desde nuestro punto de visión). 
Ninguna de las opciones anteriores es correcta. 
"Incorrecto" 10 
Para el siguiente diagrama fasorial, ¿cuales de las afirmaciones son correctas? * T,) 
(5/5 Points) 
El fasor rojo corresponde en un circuito RLC serie a la tensión compuesta del capacitor y de la resistencia. v/ 
El fasor rojo corresponde en un circuito RLC serie a la tensión compuesta de la inductancia y la resistencia. 
El fasor rojo corresponde en un circuito RLC serie a la tension compuesta de la inductancia y el capacitor. 
El fasor rojo corresponde en un circuito RLC paralelo a la tensión compuesta del capacitor y de la resistencia. 
El fasor rojo corresponde en un circuito RLC paralelo a la tensión compuesta de la inductancia y la 
resistencia. 
El fasor rojo corresponde en un circuito RLC paraleo a la tension compuesta de la inductancia y el capacitor. V 
V 
x 
La siguiente señal cuadrada tiene un ciclo de trabajo del 50%. ¿Cuáles son los resultados de 
duplicar el valor pico y llevar a la mitad de tiempo al periodo T? * 
(5/10 Points) 
El valor medio se incrementa. v/ 
El valor medio se mantiene constante. 
El valor medio disminuye. 
El valor eficaz aumenta v/ 
El valor eficaz se mantiene constante. 
El valor eficaz disminuye 
"Parcialmente correcto" 15 
La fuerza electromotriz total aplicada con 50Hz a un circuito serie de una reactancia inductiva 
pura con lmHy y una reactancia capacitiva pura con lmF resultará: * 
(10/10 Points) 
Mayor que la caída de potencial capacitiva. 
Menor que la caída de potencial inductiva. 
Igual que la diferencia entre las caldas inductiva y capacitiva. 
Mayor que la suma entre las caídas inductiva y capacitiva. ¿Cuál es el resultado sobre la recta de entrehierro que trazamos sobre la curva B_H del 
material ferromagnético al incrementar la separación del entrehierro? * 
(0/5 puntos) 
27 
50.4e/cm 
1 
IOOAe•'cm 
La recta de entrehierro aumenta su pendiente. 
La recta de entrehierro mantiene su pendiente. 
La recta entrehierro disminuye su pendiente, 
Ninguna de las opciones anteriores es correcta 
"lncorrecto" En un circuito RLC serie se miden 800W, con una corriente de IDA. Si las reactancias inductiva 
y capacitiva son respectivamente 8 y 20hms, mostrar cómo determinamos la tensión del 
generador. CF 
(5/10 puntos) 
Primero debe hallar Z. impedancia total del circuito. Luego con la LEY de Ohm se halla 
"¿Cómo hallamos la impedancia Z?"

 

Modelo 1

Friday, August 12, 2022

3:32 PM

 

<<modelo 1.pdf>>

 

Modelo 2

Friday, August 12, 2022

3:32 PM

 

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Modelo 3 - Final Regular

Friday, August 12, 2022

3:32 PM

 

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Modelo 4 - Previo

Friday, August 12, 2022

3:33 PM

 

<<modelo 4.pdf>>Ink Drawings
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Modelo 5 - Previo

Friday, August 12, 2022

3:33 PM

 

<<MODELO 5.pdf>>

 

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MODELO 6

Friday, August 12, 2022

3:33 PM

 

<<MODELO 6.pdf>>

 

Modelo 7 - Final Adelantado

Friday, August 12, 2022

3:33 PM

 

<<MODELO 7.pdf>>Ink Drawings
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