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Chapter 2 Circuit element

1. Voltage and current sources.

2. Electrical resistance (Ohm’s law).

3. Construction of a circuit model.

4. Kirchhoff’s laws.

5. Analysis of a circuit containing dependent sources.

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2.1 Voltage and current sources

• Electrical source : a device that is capable of converting nonelectric energy to electric energy and vice versa.

• Ideal voltage source (2.1(a)) : a circuit element that maintains a prescribed voltage across its terminals regardless of the current flowing in those terminals.

• Ideal current source (2.1(b)) : a circuit element that maintains a prescribed current through its terminals regardless of the voltage across those terminals.

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Voltage and current sources

• Independent source (2.1) : a voltage or current source in a circuit without relying on voltages or currents elsewhere in the circuit.

• Dependent source (controlled source ; 2.2) : a voltage or current source whose value depends on voltages or currents elsewhere in the circuit.

• Ideal dependent voltage-controlled voltage source (2.2(a)) :

.s xv v

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Voltage and current sources

• Ideal dependent current-controlled voltage source (2.2(b)) :

• Ideal dependent voltage-controlled current source (2.2(c)) :

• Ideal dependent current-controlled current source (2.2(d)) :

• Active element : a device capable of generating electric energy.

• Passive device : a device that cannot generate electric energy.

.s xv i

.s xi v

.s xi i

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2.1

• (a) : valid; (b) : valid;

(c) : not permissible;

(d) : not permissible;

(e) : valid.

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2.2

• (a) : invalid; (b) : valid; (c) : valid; (d) : invalid.

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2.2 Electric resistance (Ohm’s law)

• Resistance : the capacity of materials to impede or resist the flow of current.

• Resistor (2.5) : a circuit element used to model above behavior.

• Ohm’s law (2.6) :

(figure 2.6(a)), where

the voltage in volts,

the current in amperes,

the resistance in ohms.

(figure 2.6(b)).

v iR

v

i

R

v iR

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Electric resistance (Ohm’s law)

• Current as a function of the voltage :

• Conductance (siemens (S), mho( )) : the reciprocal of the resistance.

• Power at the terminals of a resistor :

(figure 2.6(a)), (figure 2.6(b)).v v

i iR R

1 S.G

R

2 22 2

2 22 2

( ) (figure 2.6(a)),

( ) (figure 2.6(b)).

v ip vi iR i i R v G

R G

v ip vi iR i i R v G

R G

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2.3

2 22 2

25

50 (50)2 A, ( 2) (25) 100 W.

25 25d d

d d

v vi P i R

R R

2 22 2

8

(1)(8) 8 V,

(8)(1) (8) 8 W.

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a

aa

v iR

vp i R

R

2 20.2

(50)(0.2) 10 A,

(50) (0.2) 500 W.

b b

S b

i v G

P v G

2 22 2

20

(1)(20) 20 V,

( 20)(1) (20) 20 W.

20

c c

cc

v i R

vP i R

R

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2.3 Construction of a circuit model;

• 2.9 flashlight circuit

• 2.10 switch. Short circuit : R=0;

• open circuit : R=infinity.

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2.5

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2.4 Kirchhoff’s laws

• Node : a point where two or more circuit elements meet.

• 2.15 flashlight circuit model Ohm’s law :

• Kirchhoff’s current law (KCL) : the algebraic sum of all the currents at any node in a circuit equals zero.

• 2.15 node KCL :

1 1 1, , .c c c l l lv i R v i R v i R

1 1

1

node a 0, node b 0, node c 0, node d 0;

Thus, .s c c l l s

s c l

i i i i i i i i

i i i i

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Kirchhoff’s laws

• Path : a trace of adjoining basic elements with no elements include more than once.

• Closed path (loop) : a path whose last node is the same as the starting node.

• Kirchhoff’s voltage law (KVL) : the algebraic sum of all the voltages around any closed path in a circuit equals zero.

• 2.15 KVL :

• The elements are in series when just two elements connect at a single node.

1 0.l c sv v v v

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• 2.16 KCL :

• 2.17KVL :

1 4 2 5

2 3 1

3 4

5

node a 0,

node b 0,

node c 0,

node d 0.

b a

b c

a c

i i i i

i i i i i

i i i i

i i i

1 2 4 3

3 5

4 6 5

1 2 7

path a 0,

path b 0,

path c 0,

path d 0.

b

a

b c

a c d

v v v v v

v v v

v v v v v

v v v v v v

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2.8

• 2.19 KCL& KVL.

1 1

1

6 0, 120 10 50 0;

3 A and 3 A.o o

o

i i i i

i i

2 250 10

120V

6A 1 1 1

50 10 120V 6A

(3) 50 450 W, ( 3) (10) 90 W,

120 120( 3) 360 W,

(6) 150(6) 900 W, 50 150 V.

0.

o

p p

p i

p v v i

p p p p

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2.9

2.21(b) for 10ohm :

30 5 .t tv i

2 210

30 5 10 , 2 A;

(2) (10) 40 W.

t t ti i i

p i R

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2.9

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2.5 Analysis of a circuit containing dependent sources

• 1. Once we know , we can calculate using Ohm’s law.

2. Once we know , we also know the current supplied by the

dependent source .

3. The current in the 500 V source is .

0i 0v

i5i

i

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Analysis of a circuit containing dependent sources

• 2.22 loop KVL :

• Node b KCL :

500 5 20 .oi i

5 6 .oi i i i

4 A, 24 A,

20 480 V.o

o o

i i

v i

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2.10

• 2.23 Kirchhoff’s law Ohm’s law.

• KVL :

• Ohm’s law :

• Power :

10 6 , 3 2 3 ; 1.67 A, 1 A.s s o o s oi i i i i i 3 3 V.o ov i

10 3

2 2 26 2 3

10 3 6 2 3

(10)( 1.67) 16.7 W, (3 )( ) (5)( 1) 5 W,

(1.67) (6) 16.7 W, (1) (2) 2 W, (1) (3) 3 W.

16.7 5 16.7 2 3 0 W.

s

s

V i s o

V i

p p i i

p p p

p p p p p

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2.11

• 2.24 transistor amplifier base current

• KCL :

• Dependent source constraint :

• KVL :

Bi

1 2 1(1) 0, (2) 0, (3) 0.C CC B E B Ci i i i i i i i i

(4) .C Bi i

0 2 2

1 1 2 2

(5) 0,

(6) 0.E E

CC

V i R i R

i R V i R

2 1 2

1 2 1 2

( ) /( ).

( ) /( ) (1 )CC o

BE

V R R R Vi

R R R R R