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

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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

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Associação de fontes

Robert L. Boylestad

Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.

Upper Saddle River, New Jersey 07458

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Associação de fontes

Robert L. Boylestad

Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.

Upper Saddle River, New Jersey 07458

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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

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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

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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

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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

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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

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Mesma tensão, corrente

dividida

Robert L. Boylestad

Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.

Upper Saddle River, New Jersey 07458

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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

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Lei das correntes

de Kirchhoff

Robert L. Boylestad

Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.

Upper Saddle River, New Jersey 07458

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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

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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

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Pelo método de malhas:

Robert L. Boylestad

Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.

Upper Saddle River, New Jersey 07458

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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

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Ponte equilibrada

Robert L. Boylestad

Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.

Upper Saddle River, New Jersey 07458

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Transformação Y –Δ (T – π)

Robert L. Boylestad

Introductory Circuit Analysis, 10ed.Copyright ©2003 by Pearson Education, Inc.

Upper Saddle River, New Jersey 07458

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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