irwin01_001-024hr.

qxd 30-06-2010 13:16 Page 17

BASIC CONCEPTS

SUMMARY
•
■ The standard prefixes employed ■ The passive sign convention The passive sign
p = 10-12 k = 103 convention states that if the voltage and current associated
with an element are as shown in Fig. 1.11, the product of
n = 10-9 M = 106
v and i, with their attendant signs, determines the
␮ = 10-6 G = 109 magnitude and sign of the power. If the sign is positive,
m = 10-3 T = 1012 power is being absorbed by the element, and if the sign is
negative, the element is supplying power.
■ The relationships between current and
■ Independent and dependent sources An
charge
ideal independent voltage (current) source is a two-terminal
element that maintains a specified voltage (current) between
dq(t) t
i(t) = or q(t) = i(x) dx its terminals, regardless of the current (voltage) through
dt 3-q (across) the element. Dependent or controlled sources
generate a voltage or current that is determined by a voltage
■ The relationships among power, energy, or current at a specified location in the circuit.
current, and voltage
dw ■ Conservation of energy The electric circuits
p = = vi under investigation satisfy the conservation of energy.
dt
t2 t2
¢w = p dt = vi dt ■ Tellegen’s theorem The sum of the powers
3t1 3t1 absorbed by all elements in an electrical network is zero.

1.1 If the current in an electric conductor is 2.4 A, how

many coulombs of charge pass any point in a 30-second
interval?

1.2 Determine the time interval required for a 12-A battery

charger to deliver 4800 C.

1.3 A lightning bolt carrying 30,000 A lasts for 50 micro-

seconds. If the lightning strikes an airplane flying at
20,000 feet, what is the charge deposited on the plane?

1.4 If a 12-V battery delivers 100 J in 5 s, find (a) the amount

of charge delivered and (b) the current produced.
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1.5 The current in a conductor is 1.5 A. How many coulombs of

charge pass any point in a time interval of 1.5 minutes?
1.6 If 60 C of charge pass through an electric conductor in
30 seconds, determine the current in the conductor.
1.7 Determine the number of coulombs of charge produced by
a 12-A battery charger in an hour.
1.8 Five coulombs of charge pass through the element in
Fig. P1.8 from point A to point B. If the energy absorbed by
the element is 120 J, determine the voltage across the
element.
B
+
V1
-

A
Figure P1.8

1.9 The current that enters an element is shown in

Fig. P1.9. Find the charge that enters the element
in the time interval 0 6 t 6 20 s.

i(t) mA

10

0 10 20 t (s)
Figure P1.9

1.10 The charge entering the positive terminal of an element is

q(t) = -30e-4t mC. If the voltage across the element is
120e-2t V, determine the energy delivered to the element
in the time interval 0 6 t 6 50 ms.

1.15 The energy absorbed by the BOX in Fig. P1.15 is shown below. How much charge enters
the BOX between 0 and 10 milliseconds?
w(t) (mJ)
15
i (t)
10

15 V + BOX
– 5

1 2 3 4 5 6 7 8 9 10 t (ms)
–5

–10

–15
Figure P1.15
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1.11 The charge entering the positive terminal of an element is

given by the expression q(t) = -12e-2t mC. The power
delivered to the element is p(t) = 2.4e-3t W. Compute
the current in the element, the voltage across the element,
and the energy delivered to the element in the time
interval 0 6 t 6 100 ms.
1.12 The voltage across an element is 12e-2t V . The current
entering the positive terminal of the element is 2e-2t A.
Find the energy absorbed by the element in 1.5 s starting
from t ⫽ 0.
1.13 The power absorbed by the BOX in Fig. P1.13 is
2e-2t W. Calculate the amount of charge that enters the
BOX between 0.1 and 0.4 seconds.

4e–t V + BOX
–

Figure P1.13

1.14 The power absorbed by the BOX in Fig. P1.14 is

0.1e-4t W. Calculate the energy absorbed by the BOX
during this same time interval.

10e–2t V + BOX
–

Figure P1.14

1.15 The energy absorbed by the BOX in Fig. P1.15 is shown below. How much charge enters
the BOX between 0 and 10 milliseconds?
w(t) (mJ)
15
i (t)
10

15 V + BOX
– 5

1 2 3 4 5 6 7 8 9 10 t (ms)
–5

–10

–15
Figure P1.15
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PROBLEMS 19

1.16 The charge that enters the BOX in Fig. P1.16 is shown in the graph below. Calculate and sketch
the current flowing into and the power absorbed by the BOX between 0 and 10 milliseconds.

i (t)

12 V + BOX
–

q(t) (mC)
3

1 2 3 4 6 7 8 9 10 t (ms)
–1

–2

–3
Figure P1.16

1.17 The energy absorbed by the BOX in Fig. P1.17 is given below. Calculate and sketch the
current flowing into the BOX. Also calculate the charge which enters the BOX between 0
and 12 seconds.

i (t)

10 V + BOX
–

w(t) (J)

6 7 8 10 12

1 2 3 4 5 9 11 t (s)
–2.5

Figure P1.17
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20 CHAPTER 1 BASIC CONCEPTS

1.18 The charge entering the upper terminal of the BOX in Fig. P1.18 is shown below. How much
energy is absorbed by the BOX between 0 and 9 seconds?
i (t)

12 V + BOX
–

q(t) (C)

0.5

1 2 3 4 5 6 7 8 9 t (s)
–0.5

–1

–1.5

Figure P1.18

1.19 The energy absorbed by the BOX in Fig. P1.19 is shown in the graph below. Calculate and
sketch the current flowing into the BOX between 0 and 10 milliseconds.
i (t)

12 V + BOX
–

w(t) (mJ)
30

20

10

5 6 7

1 2 3 4 8 9 10 t (ms)
–10

–20

–30

Figure P1.19
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1.20 Determine the amount of power absorbed or supplied

by the element in Fig. P1.20 if
(a) V1 = 9 V and I = 2A
(b) V1 = 9 V and I = -3A
(c) V1 = -12 V and I = 2A
(d) V1 = -12 V and I = -3A

+ I
V1
-

Figure P1.20

1.21 Calculate the power absorbed by element A in

Fig. P1.21.

3A

–
15 V A
+

Figure P1.21

1.22 Calculate the power supplied by element A in Fig. P1.22.

2A

+
20 V A
–

Figure P1.22

1.23 Element A in the diagram in Fig. P1.23 absorbs 30 W of

power. Calculate Vx.

2A

+
Vx A
–

Figure P1.23
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1.24 Element B in the diagram in Fig. P1.24 supplies 60 W of

power. Calculate Ix.

–
24 V B
+

Ix
Figure P1.24

1.25 Element B in the diagram in Fig. P1.25 supplies 72 W of

power. Calculate VA.

3A

+
VA B
–

Figure P1.25

1.26 Element B in the diagram in Fig. P1.26 supplies 72 W of

power. Calculate Ix.

+
18 V B
–

Ix
Figure P1.26

1.27 (a) In Fig. P1.27 (a), P1 = 36 W. Is element 2 absorbing

or supplying power, and how much?
(b) In Fig. P1.27 (b), P2 = -48 W. Is element 1 absorb-
ing or supplying power, and how much?

+ -
1 12 V 1 6V
– +
+ +
2 6V 2 24 V
- -

(a) (b)
Figure P1.27
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1.28 Two elements are connected in series, as shown in

Fig. P1.28. Element 1 supplies 24 W of power. Is ele-
ment 2 absorbing or supplying power, and how much?

+
1 3V
–
-
2 6V
+

Figure P1.28

1.29 Element 2 in Fig. P1.29 absorbed 32 W. Find the power

absorbed or supplied by elements 1 and 3.

-
1 4V
+
+
2 8V
–
+
3 12 V
-

Figure P1.29

1.30 Choose Is such that the power absorbed by element 2 in

Fig. P1.30 is 7 W.
4V
+ –
1
+ +
6V Is 2 2V
– –

Figure P1.30
1.31 Find the power that is absorbed or supplied by the circuit
elements in Fig. P1.31.

6V
+ - 2A
1

+
20 V 2A + 14 V
-
-
2A

(a)

8V
Ix=4 A + -
1

+
16 V 4A + 2Ix
-
-
4A

(b)

Figure P1.31
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1.32 Find the power that is absorbed or supplied by the net-

work elements in Fig. P1.32.
8V
Ix=2 A + - 2A
1

12 V ± ± 2Ix
– –
2A

(a)

24 V 20 V
+ -
–± 1
2A 2A Ix=2 A
+
± 4Ix 2 12 V
–
-
2A

(b)

Figure P1.32
1.33 Compute the power that is absorbed or supplied by the
elements in the network in Fig. P1.33.

12 V 1Ix
+ -
Ix=4 A 2A
1 –±
2A
+ +
± 2 24 V 3 28 V
36 V –
- -

Figure P1.33
1.34 Find the power that is absorbed or supplied by element 2
in Fig. P1.34.

4V 2Vx
2A+ –
1 –+
+
12 V + 2 Vx
–
–
2A

Figure P1.34
1.35 Find Ix in the network in Fig. P1.35.

1Ix
Ix +12 V –
1 –+
2A 2A
+ +
36 V + 2 24 V 3 28 V
–
– –

Figure P1.35
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1.36 Determine the power absorbed by element 1 in Fig. P1.36.

Ix 12 V 8V
+ – + –
1 2
2A
+ +
36 V + 24 V 2Ix 3 16 V
– – –

Figure P1.36

1.37 Find the power absorbed or supplied by element 1 in

Fig. P1.37.

6V 4V
+ – + –
1 2
Ix 2A
+
18 V + 24 V + 2Ix 20 V
– –
–
Ix

Figure P1.37

1.38 Find the power absorbed or supplied by element 3 in

Fig. P1.38.

4V 12 V
+ –
1 –+
4A
+
2A
2 16 V
–
+
+ 12 V + 2Vx 4 20 V
– – –
+

2A
3 Vx 2A
–
2A

Figure P1.38

1.39 Find the power absorbed or supplied by element 1 in Fig.

P1.39.

4V 12 V
+ –
1 –+
4A
+ + + +
4Ix 12 V 2 8V 3 20 V 4 20 V
– – – –
4A 2A Ix

Figure P1.39
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1.40 Find Vx in the network in Fig. P1.40 using Tellegen’s

theorem.
16 V
2A + -
1 -+ 2 3
+ - +
12 V 24 V Vx -
- -
9V + + 12 V

Figure P1.40
1.41 Find Ix in the circuit in Fig. P1.41 using Tellegen’s
theorem.

4V 8V 18 V 12 V
2 A+ - + - + - ±–
2A Ix Ix
+ +
± 24 V 12 V 2A 6V
–
- -

Figure P1.41
1.42 Is the source Vs in the network in Fig. P1.42 absorbing
or supplying power, and how much?

6V VS
+ -
-+
3A 9A 6A
- - -
10 V 9A 16 V 8V
+ + +
3A

Figure P1.42
1.43 Find Io in the network in Fig. P1.43 using Tellegen’s
theorem.
8V
6 A+ -
1
4A
+
± 2 10 V Ix=2 A
24 V –
-
6V +
- +
3 4 16 V
Io -
+
4Ix ± 5 6V
–
-
8V
3A - + 1A
6
3A
Figure P1.43
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24 CHAPTER 1 BASIC CONCEPTS

1.44 Calculate the power absorbed by each element in the

circuit in Fig. P1.44. Also verify Tellegen’s theorem is
satisfied by this circuit.

3Ix 24 V
+ –
–+ 5
2A

2A

12 V 6V 9V
+ – + – - +
1 2 4
2A 4A
4A
+ +
24 V + 6A 6V 3 15 V +
– 12 V –
– –
4A Ix = 2 A

Figure P1.44
1.45 Calculate the power absorbed by each element in the cir-
cuit in Fig. P1.45. Also verify that Tellegen’s theorem is
satisfied by this circuit.
10 V
4A + –
3

5V 5V
+ – + –
2 4
1A 3A

40 V + 15 V +
– + –
5A 30 V 4A
- + 1A
–
5V 1 10 V 5
+ –

Figure P1.45

1.46 In the circuit in Fig. P1.46, element 1 absorbs 40 W, ele-

ment 2 supplies 50 W, element 3 supplies 25 W, and ele-
ment 4 absorbs 15 W. How much power is supplied by
element 5?

1 2

3 4 5

Figure P1.46