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2. Análise de Circuitos Elétricos
Simples
Redes e circuitos;
Lei de Ohm;
Fontes independentes e dependentes;
Leis de Kirchhoff;
Associação de resistores e fontes;
Divisores de tensão e corrente.
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Ex.: Obter I.
8 mA
Calcule a tensão que tem que ser aplicada
ao ferro de solda, mostrado abaixo, para
estabelecer uma corrente de 1,5 A, sendo a
sua resistência interna de 80 Ω.
. (1,5 A) (80 ) 120 VE I R x
Gráfico da Lei de Ohm
VR
I
Gráfico da Lei de Ohm
Gráfico da Lei de Ohm
Gráfico da Lei de OhmDetermine a resistência associada ao gráfico abaixo e compare
com a Lei de Ohm.
Para V = 6V e I = 3mA
3
62 k
3 10cc
VR
I x
Para o intervalo entre 6V e 8V
3
22 k
1 10
VR
I x
Diodo Semicondutor
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Potência Elétrica
2
2
. .
.
VP
P V I V R I R
P R I
Para o exemplo do ferro de solda:
2. (80 ).(1,5A) 180 WP R I
A curva característica I – V de uma lâmpada de
filamento é mostrada a seguir. Se a tensão nominal de
operação da lâmpada é 120 V, determine a potência
dissipada e sua resistência.Solução:
. (120).(0,625) 75 W
120192
0,625
P V I
VR
I
Obs.: e .P
I V P RR
Potência
Fornecida Consumida
Eficiência
o dissipadaiP P P
o o
o
Eficiência = = (%) = 100%
(%) = 100%
i i
i
P Px
P P
Wx
W
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
o(%) = 100%i
Wx
W
Wattímetros
Um motor de 2 hp opera com eficiência de
75%. Qual a potência de entrada em watts?
Se a tensão aplicada ao motor é 220 V,
qual a corrente na entrada?
Solução: o(%) 100%
(2hp).(746 W/ hp)0,75
1.492 W1.989,33 W
0,75
i
i
i
Px
P
P
P
1.989,33. 9,04 A
220
ii
PP E I I
E
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
o1 o2 o3total 1 2 3
1 2 3i i i
P P P
P P P
Energia (W)
(W). (s)Energia(kWh) =
1.000
P t
Energia (W)
(W). (s)Energia(kWh) =
1.000
P t
Calcule a quantidade de energia (em kWh) necessária para
manter uma lâmpada de filamento (60 W) acesa continuamente
durante um ano.
. (60W).(24h/dia).(365dias)
1000 1000
525.600(Wh)525,6 kWh
1000
P tW
W
Medir de tensão - voltímetro
Medir de tensão - voltímetro
Medir corrente - amperímetro
(a) Measuring the no-load voltage E; (b) measuring the
short-circuit current.
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Segurança – categorias:
Segurança – categorias:
Multímetros digitais
Amperímetros
Fonte independente
Fonte independente - práticas
. .p L p LE E R I E E R I
Toda fonte prática tem
uma resistência
interna, responsável
pela dissipação (queda
de tensão nominal).
Fonte independente - práticas
L Ls s L L s
s
L ss L s L
s
R IE R I R I I
R
R RI I I I I
R
Conversão de fonte
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Conversão de fonte
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Conversão de fonte
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Associação de fontes
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Associação de fontes
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Ex.: Obter a corrente destacada na figura.
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
1 1
1
4.3 12 V
3
s
s
E I R
R R
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
1 1
1
4.3 12 V
3
s
s
E I R
R R
1 22
2
173,4 A
5s
E EI
R R
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Fontes de correntes de diferentes intensidades
não podem ser ligadas em série.
Fonte de corrente dependente
Ex.: Transistor bipolar
Classificação
2V 2. 4V
1,5A
. (4V).(1,5A) 6W
c d c
d
d d d
v v v
i
P v i
Determinação do número de vezes
que a Lei de Kirchhoff para correntes
deve ser aplicada
Ligação série
Ligação paralelo
Circuito série
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Determinar a resistência total e a
corrente para cada circuito abaixo
6020 3 A
20TR I
101,63 M 6,135 A
1,63 MTR I
35110 318,2 mA
110TR I
12010 k 12 mA
10kTR I
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Determinar a resistência desconhecida
e a corrente I
10 12 8
301 A
30
TR R
I
Ilustrar o divisor de
tensão
3 3
1 2 3 T
R RV E E
R R R R
Circuito paralelo
Paralelo - Série
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Mesma tensão, corrente
dividida
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Obter as correntes e a
resistência equivalente
Ilustrar o divisor de corrente
2 21
1 2
S S
T
R RI I I
R R R
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Obter as correntes,
resistência e tensão
Lei das correntes de
Kirchhoff
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Lei das correntes
de Kirchhoff
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Lei das correntes
de Kirchhoff
Lei das correntes
de Kirchhoff
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Lei das correntes
de Kirchhoff
2 A
4 A
2 A
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Exemplo
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Exemplo
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Análise de malhas – complicado?
Circuito em ponte
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Condição de
equilíbrio para o
circuito em
ponte
1 21 4 2 3
3 4
R RR R R R
R R
50RV
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Pelo método de malhas:
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Ponte equilibrada
1 21 4 2 3
3 4
R RR R R R
R R
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Ponte equilibrada
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Transformação Y –Δ (T – π)
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Conceito Y –Δ
Obtenção da resistência Ra-c
a-c a-c a-c 1 3
a-b 1 2 b-c 2 3
( )(Y) ( )
( ) ( ) e
B A C
B A C
C A B A B C
C A B A B C
R R RR R R R R
R R R
R R R R R RR R R R R R
R R R R R R
Obtenção da resistência
1 2 1 3 2 33
3
1 2 1 3 2 31
1
1 2 1 3 2 32
2
A BC
A B C
C BA
A B C
A CB
A B C
R R R R R RR RR R
R R R R
R R R R R R R RR R
R R R R
R R R R R R R RR R
R R R R
Robert L. Boylestad
Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Exemplo
Observação:
Y 3
A B C
RR R R R
Exemplo
Exemplo