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Circuits Ulaby Solutions Chapter 1

Transcript of Circuits Solutions

• Problem 1.1 Use appropriate multiple and submultiple prefixes to express thefollowing quantities:

(a) 3,620 watts (W)(b) 0.000004 amps (A)(c) 5.2106 ohms ()(d) 3.91011 volts (V)(e) 0.02 meters (m)(f) 32105 volts (V)

Solution:(a) 3,620 W = 3.62 kW.(b) 0.000004 A = 4 A.(c) 5.2106 = 5.2 .(d) 3.91011 V = 390 GV.(e) 0.02 m = 20 mm.(f) 32105 V = 3.2 MV.

• Problem 1.2 Use appropriate multiple and submultiple prefixes to express thefollowing quantities:

(a) 4.71108 seconds (s)(b) 10.3108 watts (W)(c) 0.00000000321 amps (A)(d) 0.1 meters (m)(e) 8,760,000 volts (V)(f) 3.161016 hertz (Hz)

Solution:(a) 4.71108 s = 47.1 ns.(b) 10.3108 W = 1.03 GW.(c) 0.00000000321 A = 3.21 nA.(d) 0.1 = 10 cm.(e) 8,760,000 V = 8.76 MV.(f) 3.161016 Hz = 316 aHz.

• Problem 1.3 Convert:(a) 16.3 m to mm(b) 16.3 m to km(c) 4106 F (microfarad) to pF (picofarad)(d) 2.3 ns to s(e) 3.6107 V to MV(f) 0.03 mA (milliamp) to A

Solution:(a) 16.3 m = 16,300 mm.(b) 16.3 m = 0.0163 km.(c) 4106 F = 4 pF.(d) 2.3 ns = 2.3103 s.(e) 3.6107 V = 36 MV.(f) 0.03 mA = 30 A.

• Problem 1.4 Convert:(a) 4.2 m to m(b) 3 hours to seconds(c) 4.2 m to km(d) 173 nm to m(e) 173 nm to m(f) 12 pF (picofarad) to F (farad)

Solution:(a) 4.2 m = 4.2106 m.(b) 3 hours = 1.081010 s.(c) 4.2 m = 4.2103 km.(d) 173 nm = 1.73107 m.(e) 173 nm = 0.173 m.(f) 12 pF = 1.21011 F.

• Problem 1.5 For the circuit in Fig. P1.5:(a) Identify and label all distinct nodes.(b) Which of those nodes are extraordinary nodes?(c) Identify all combinations of 2 or more circuit elements that are connected in

series.(d) Identify pairs of circuit elements that are connected in parallel.

4 5 2

1 3

16 V+

_

Figure P1.5: Circuit for Problem 1.5.

Solution:

4 5 2

1 3

16 V+

_

a b

d

c

Fig. P1.5 (a)

(a) Nodes identified in Fig. P1.5(a).(b) Nodes b, c, and d are extraordinary.(c) Series connections: 16 V and 1 .(d) Parallel connections: 4 and 5 .

• Problem 1.6 For the circuit in Fig. P1.6:(a) Identify and label all distinct nodes.(b) Which of those nodes are extraordinary nodes?(c) Identify all combinations of 2 or more circuit elements that are connected in

series.(d) Identify pairs of circuit elements that are connected in parallel.

2

4 4

8 V12 V+

_

+

_

+

_

+

_

Figure P1.6: Circuit for Problem 1.6.

Solution:

Fig. P1.6 (a)

2

4 4

8 V12 V+

_

+

_

+

_

+

_

a b

d

c

(a) Nodes identified in Fig. P1.6(a).(b) Nodes b and d are extraordinary.(c) Series connections: 12 V and 4

4 and 8 V.(d) Parallel connections: none.

• Problem 1.7 For the circuit in Fig. P1.7:(a) Identify and label all distinct nodes.(b) Which of those nodes are extraordinary nodes?(c) Identify all combinations of 2 or more circuit elements that are connected in

series.(d) Identify pairs of circuit elements that are connected in parallel.

1 0.1

0.2

0.3

0.4

1 4 V

+

_

Figure P1.7: Circuit for Problem 1.7.

Solution:

Fig. P1.7 (a)

1 0.1

0.2

0.3

0.4

1 4 V

+

_

ba

e

c d

(a) Nodes identified in Fig. P1.7(a).(b) Nodes b, c, d, and e are extraordinary.(c) Series connections: 4 V and 1 .(d) Parallel connections: None.

• Problem 1.8 For the circuit in Fig. P1.8:(a) Identify and label all distinct nodes.(b) Which of those nodes are extraordinary nodes?(c) Identify all combinations of 2 or more circuit elements that are connected in

series.(d) Identify pairs of circuit elements that are connected in parallel.

25 40

30

10

20

60 5

12 V

15

+

_

Figure P1.8: Circuit for Problem 1.8.

Solution:

Fig. P1.8 (a)

25 40

30

10

20

60 5

12 V

15

+

_

a b

e

f c d

(a) Nodes identified in Fig. P1.8(a).(b) Nodes b, c, e, and f are extraordinary.(c) Series connections: 12 V and 25

10 and 20 (d) Parallel connections: None.

• Problem 1.9 For the circuit in Fig. P1.9:(a) Identify and label all distinct nodes.(b) Which of those nodes are extraordinary nodes?(c) Identify all combinations of 2 or more circuit elements that are connected in

series.(d) Identify pairs of circuit elements that are connected in parallel.

3 6

2 2 4

4 A

48 V+

_

Figure P1.9: Circuit for Problem 1.9.

Solution:

3 6

2

2 4

4 A

48 V+

_

b

e

a

d

c

Fig. P1.9 (a)

(a) Nodes identified in Fig. P1.9(a).(b) Nodes a, b, c, and e are extraordinary.(c) Series connections: 2 and 48 V.(d) Parallel connections: None.

• Problem 1.10 For the circuit in Fig. P1.10:(a) Identify and label all distinct nodes.(b) Which of those nodes are extraordinary nodes?(c) Identify all combinations of 2 or more circuit elements that are connected in

series.(d) Identify pairs of circuit elements that are connected in parallel.

6 16

32 8

4 12 V+

_

Figure P1.10: Circuit for Problem 1.10.

Solution:

6 16

32

10

8

4 12 V+

_

a b c d

b

Fig. P1.10 (a)

(a) Nodes identified in Fig. P1.10(a).(b) Nodes b and c are extraordinary.(c) Series connections: 8 and 6 .(d) Parallel connections: 12 V and 4

4 and short circuit.

• Problem 1.11 For the circuit in Fig. P1.11:(a) Identify and label all distinct nodes.(b) Which of those nodes are extraordinary nodes?(c) Identify all combinations of 2 or more circuit elements that are connected in

series.(d) Identify pairs of circuit elements that are connected in parallel.

6

2

4

3

1

5 20 V

+

_

+

_

Figure P1.11: Circuit for Problem 1.11.

Solution:

6

2

4

3

1

5 20 V

+

_

e

c d

b

a

Fig. P1.11

(a) Nodes identified in Fig. P1.11(a).(b) Nodes a, b, and d are extraordinary.(c) Series connections: 5 and 20 V

4 and 6 .(d) Parallel connections: 2 and 1 .

• Problem 1.12 The total charge contained in a certain region of space is 1 C. Ifthat region contains only electrons, how many does it contain?

Solution:ne =

Qqe

=

11.61019 = 6.2510

18 electrons.

• Problem 1.13 A certain cross section lies in the xy plane. If 3 1020 electronsgo through the cross section in the z-direction in 4 seconds, and simultaneously,1.51020 protons go through the same cross section in the negative z-direction, whatis the magnitude and direction of the current flowing through the cross section?

Solution: Negatively charged electrons moving along +z-direction constitute acurrent in the z-direction:

Ie =Qt =

310201.610194

= 12 A, along z-direction.

Positively charged protons moving along z-direction constitute a current in thez-direction:

Ip =Qt =

1.510201.610194

= 6 A, along z-direction.

Total net current is:

I = Ie + Ip = 12+6 = 18 A, along z-direction.

• Problem 1.14 Determine the current i(t) flowing through a resistor if thecumulative charge that has flowed through it up to time t is given by

(a) q(t) = 3.6t mC(b) q(t) = 5sin(377t) C(c) q(t) = 0.3[1 e0.4t ] pC(d) q(t) = 0.2t sin(120pit) nC

Solution:(a) i(t) = dqdt = ddt (3.6t103) = 3.6103 = 3.6 (mA).(b) i(t) = dqdt = ddt [(5sin377t)106] = 5377106 cos377t = 1.885cos377t(mA).(c) i(t) = dqdt = ddt [0.3(1 e0.4t)1012] = 0.31012 (0.4) (e0.4t)

= 0.12e0.4t (pA).(d) i(t) = dqdt = ddt [(0.2t sin120pit)109]

= (0.2sin120pit +0.2t120pi cos120pit)109

= 0.2sin120pit +75.4t cos120pit (nA).

• Problem 1.15 Determine the current i(t) flowing through a certain device if thecumulative charge that has flowed through it up to time t is given by

(a) q(t) =0.45t3 C(b) q(t) = 12sin2(800pit) mC(c) q(t) =3.2sin(377t)cos(377t) pC(d) q(t) = 1.7t[1 e1.2t ] nC

Solution:(a)

i(t) =dqdt =

ddt [0.45t

3106] =0.453t2106 =1.35t2 (A).

(b)

i(t) =dqdt =

ddt [(12sin

2 800pit)103] = 212800pi103 sin800pit cos800pit

= 60.32sin800pit cos800pit (A).