Ch06 Solution

Irwin, Basic Engineering Circuit Analysis, 11/E 1

Chapter 06: Capacitance and Inductance Problem 6.1

SOLUTION:

6.1 An uncharged 100-μF capacitor is charged by a constant current of 1 mA. Find the voltage across the capacitor after 4 s.



SOLUTION:

6.2 A capacitor has an accumulated charge of 600 μC with 5 V across it. What is the value of capacitance?



SOLUTION:

6.3 The energy that is stored in a 25-μF capacitor is w(t) = 12 si n 2 377t J. Find the current in the capacitor.



SOLUTION:

6.4 The current in a 100-μF capacitor is shown in Fig. P6.4. Determine the waveform for the voltage across the capacitor if it is initially uncharged.

10

0 1 2

i(t) (mA)

t (ms)

Figure P6.4



SOLUTION:

6.5 The voltage across a 50-μF capacitor is shown in Fig. P6.5. Determine the current waveform.

02 4 6

8 10

10

−10

12

t (ms)

υ(t) ( V )

Figure P6.5

2 Irwin, Basic Engineering Circuit Analysis, 11/E

Problem 6.5 Chapter 06: Capacitance and Inductance



SOLUTION:

6.6 Draw the waveform for the current in a 12-μF capacitor when the capacitor voltage is as described in Fig. P6.6.

0

10

12

−8

16

6

υ(t) ( V )

t (μs)

Figure P6.6



SOLUTION:

6.7 The voltage across a 10-μF capacitor is shown in Fig. P6.7. Determine the waveform for the current in the capacitor.

2

0

4

6

4 8 12 16

υ(t) V

t (ms)

Figure P6.7



SOLUTION:

6.8 If the voltage waveform across a 100-μF capacitor is shown in Fig. P6.8, determine the waveform for the current.

5

10

5 10 15 20

υ(t) ( V )

t (ms)

Figure P6.8



SOLUTION:

6.9 The voltage across a 25-μF capacitor is shown in Fig. P6.9. Determine the current waveform.

00.2 0.4 0.6

0.8 1.0

20

−20

1.2

υ(t) ( V )

t (ms)

Figure P6.9



SOLUTION:

6.10 The voltage across a 2-F capacitor is given by the waveform in Fig. P6.10. Find the waveform for the current in the capacitor.

υC(t) ( V )

t (s)0 10 20 30 40 50

+12

−12

Figure P6.10



SOLUTION:

6.11 The voltage across a 2-μF capacitor is given by the waveform in Fig. P6.11. Compute the current waveform.

t (ms)2 3 6

−12

υ(t) ( V )

Figure P6.11



SOLUTION:

6.12 Draw the waveform for the current in a 24-μF capacitor when the capacitor voltage is as described in Fig. P6.12.

t (μs)0

100

6

−4

160

60

υ(t) (V)

Figure P6.12



SOLUTION:

6.13 The waveform for the current in a 50-μF capacitor is shown in Fig. P6.13. Determine the waveform for the capacitor voltage.

0 t (ms)

10

10 20 30 40

i(t) (mA)

Figure P6.13



SOLUTION:

6.14 The waveform for the current flowing through the 10-μF capacitor in Fig. P6.14a is shown in Fig. P6.14b. If υ c (t = 0) = 1 V, determine υ c (t) at t = 1 ms, 3 ms, 4 ms, and 5 ms.

+

10 μF

−

i(t)

(a)

υc(t)

15

−10

1 2

3

4

5

6t (ms)

(b)

i(t) (mA)

Figure P6.14



SOLUTION:

6.15 The waveform for the current in a 50-μF initially uncharged capacitor is shown in Fig. P6.15. Determine the waveform for the capacitor’s voltage.

00

10

−10

10 20 30 40 50

i(t) (mA)

t (ms)

Figure P6.15



SOLUTION:

6.16 The voltage across a 10-μF capacitor is given by the waveform in Fig. P6.16. Plot the waveform for the capaci-tor current.

−12

125 10

υ(t) (V)

t (ms)

Figure P6.16



SOLUTION:

6.17 If υ c (t = 2 s) = 10 V in the circuit in Fig. P6.17, find the energy stored in the capacitor and the power supplied by the source at t = 6 s.

0.5 F

3 Ω 6 Ω2 A

+ −υc(t)

Figure P6.17



SOLUTION:

6.18 The current in an inductor changed from 0 to 200 mA in 4 ms and induces a voltage of 100 mV. What is the value of the inductor?



SOLUTION:

6.19 The current in a 100-mH inductor is i(t) = 2 sin 377t A. Find (a) the voltage across the inductor and (b) the expression for the energy stored in the element.



SOLUTION:

6.20 The current in a 50-mH inductor is specified as follows:

i(t) = 0 t < 0

i(t) = 2t e −4t A t > 0

Find (a) the voltage across the inductor, (b) the time at which the current is a maximum, and (c) the time at which the voltage is a minimum.



SOLUTION:

6.21 The current in a 25-mH inductor is given by the expressions

i(t) = 0 t < 0

i(t) = 10(1 − e −t ) mA t > 0

Find (a) the voltage across the inductor and (b) the expression for the energy stored in it.



SOLUTION:

6.22 Given the data in the previous problem, find the voltage across the inductor and the energy stored in it after 1 s.



SOLUTION:

6.23 The voltage across a 2-H inductor is given by the waveform shown in Fig. P6.23. Find the waveform for the cur-rent in the inductor.

0 2 4 6 t (s )

5

−5

υ(t) ( V )

Figure P6.23



SOLUTION:

6.24 The voltage across a 4-H inductor is given by the waveform shown in Fig. P6.24. Find the waveform for the current in the inductor υ(t) = 0, t < 0.

0

2.4

10 20 30 40 50

υ(t) (mV)

t (ms)

Figure P6.24



SOLUTION:

6.25 The voltage across a 10-mH inductor is shown in Fig. P6.25. Determine the waveform for the inductor current.

0 1 2

10−

υ(t) ( mV )

t (ms)Figure P6.25



SOLUTION:

6.26 If the current i(t) = 1.5t A flows through a 2-H inductor, find the energy stored at t = 2 s.



SOLUTION:

6.27 The current in a 30-mH inductor is shown in Fig. P6.27. Derive the waveform for the inductor voltage.

60

120

10 20 30 40 50 60 70

i(t) (mA)

t (ms)

Figure P6.27



SOLUTION:

6.28 The current waveform in a 40-mH inductor is shown in Fig. P6.28. Derive the waveform for the inductor voltage.

5

10

15

20

2 4 6 8 10 12

i(t) (mA)

t (ms)

Figure P6.28



6.29 The waveform for the current flowing through a 0.5-H inductor is shown in the plot in Fig. P6.29. Accurately sketch the inductor voltage versus time. Determine the following quantities: (a) the energy stored in the inductor at t = 1.7 ms, (b) the energy stored in the inductor at t = 4.2 ms, and (c) the power absorbed by the inductor at t = 1.2 ms, t = 2.8 ms, and t = 5.3 ms.

5

10

−5

−10

1 2 3

4

5 6

i(t) (mA)

t (ms)

+

−

i(t) υL(t) 0.5 H

Figure P6.29

SOLUTION:



SOLUTION:

6.30 The current in a 50-mH inductor is given in Fig. P6.30. Sketch the inductor voltage.

0 t (ms)24

−100

6 8 10

100

i(t) (mA)

Figure P6.30



SOLUTION:

6.31 The current in a 24-mH inductor is given by the waveform in Fig. P6.31. Find the waveform for the voltage across the inductor.

4 511

12

−129

122

−24

i(t) (A)

t (ms)

Figure P6.31



SOLUTION:

6.32 The current in a 10-mH inductor is shown in Fig. P6.32. Determine the waveform for the voltage across the inductor.

t (ms)

0

−12

1 2 3 4 5 6

i(t) (mA)

Figure P6.32



SOLUTION:

6.33 The current in a 50-mH inductor is shown in Fig. P6.33. Find the voltage across the inductor.

i(t) (mA)

t (ms)0

−20

+10

20 40 60 8070

Figure P6.33



6.34 Draw the waveform for the voltage across a 24-mH inductor when the inductor current is given by the waveform shown in Fig. P6.34.

t (s )0.3

0.6

1.1

8

4

−2

0.9

i(t) (A)

Figure P6.34

SOLUTION:



SOLUTION:

6.35 The current in a 4-mH inductor is given by the waveform in Fig. P6.35. Plot the voltage across the inductor.

0.5 1.0

0.12

i(t) (mA)

t (ms)

Figure P6.35



SOLUTION:

6.36 The waveform for the current in the 2-H inductor shown in Fig. P6.36a is given in Fig. P6.36b. Determine the following quantities: (a) the energy stored in the inductor at t = 1.5 ms, (b) the energy stored in the inductor at t = 7.5 ms, (c) υ L (t) at t = 1.5 ms, (d) υ L (t) at t = 6.25 ms, and (e) υ L (t) at t = 2.75 ms.

i(t) 2 H

(a)

υL(t)−

+

t (ms)

7.5

30

−10

1

(b)

2 3

4 5

6 7 8

i(t) (mA)

Figure P6.36



SOLUTION:

6.37 If the total energy stored in the circuit in Fig. P6.37 is 80 mJ, what is the value of L?

200 Ω

L

80 μF 50 Ω1 A

Figure P6.37



SOLUTION:

6.38 Find the value of C if the energy stored in the capacitor in Fig. P6.38 equals the energy stored in the inductor.

200 Ω

100 Ω

0.1 H

C

12 V +–

Figure P6.38



SOLUTION:

6.39 What values of capacitance can be obtained by interconnecting a 4-μF capacitor, a 6-μF capacitor, and a 12-μF capacitor?



SOLUTION:

6.40 Given four 2-μF capacitors, find the maximum value and minimum value that can be obtained by interconnecting the capacitors in series/parallel combinations.



SOLUTION:

6.41 Determine the values of inductance that can be obtained by interconnecting a 4-mH inductor, a 6-mH inductor, and a 12-mH inductor.



SOLUTION:

6.42 Given four 4-mH inductors, determine the maximum and minimum values of inductance that can be obtained by interconnecting the inductors in series/parallel combinations.



SOLUTION:

6.43 Given a 6-, 9-, and 18-mH inductor, can they be interconnected to obtain an equivalent 12-mH inductor?



SOLUTION:

6.44 Given the network in Fig. P6.44, find the power dissi pated in the 3-Ω resistor and the energy stored in the capacitor.

2 F

4 Ω

3 Ω 3 H2 H

6 Ω 6 A12 V +−

Figure P6.44



SOLUTION:

6.45 Find the total capacitance C T in the network in Fig. P6.45. All capacitors are in microfarads.

3 4

2 4

3

4CT

Figure P6.45




CT

12

6 8

6 4

4

3

3

Figure P6.46

SOLUTION:



SOLUTION:

6.47 Find the total capacitance C T of the network in Fig. P6.47.

4 μF

1 μF

2 μF 3 μF

12 μFCT

Figure P6.47



SOLUTION:

6.48 Find C T in the network shown in Fig. P6.48.

6 μF6 μF

4 μF

8 μF

3 μF

12 μFCT

Figure P6.48



6.49 Determine the value of C T in the circuit in Fig. P6.49.

5 μF

6 μF

6 μF

12 μF

11 μF

9 μF

3 μF

CT

Figure P6.49

SOLUTION:



SOLUTION:

6.50 Find C T in the network in Fig. P6.50.

CT

3 μF3 μF

4 μF

3 μF

12 μF

6 μF

Figure P6.50



SOLUTION:


CT

3

49

3 3

6

3

Figure P6.51



SOLUTION:

6.52 Find the total capacitance C T shown in the network in Fig. P6.52.

CT 2 μF4 μF

2 μF4 μF8 μF6 μF

12 μF

Figure P6.52



SOLUTION:

6.53 Find the total capacitance C T of the network in Fig. P6.53.

4 μF6 μF

3 μF

3 μF

6 μF

CT

Figure P6.53



SOLUTION:

6.54 Find the total capacitance C T shown in the network in Fig. P6.54.

4 μF

4 μF

3 μF8 μF

4 μF 2 μF

2 μF

CT

Figure P6.54



6.55 In the network in Fig. P6.55, find the capacitance C T if (a) the switch is open and (b) the switch is closed.

6 μF

12 μF

12 μF

6 μF

3 μF

6 μFCT

Figure P6.55

SOLUTION:



SOLUTION:

6.56 Find the total capacitance CT in the network in Fig. P6.56. All capacitors are 12 microfarads.

CT

Figure P6.56



SOLUTION:

6.57 If the total capacitance of the network in Fig. P6.57 is 10 μF, find the value of C.

CT = 10 μF

C

12 μF 6 μF

4 μF

Figure P6.57



SOLUTION:

6.58 Find the value of C in Fig. P6.58.

CT = 4 μF

C

12 μF

10 μF 2 μF

3 μF

Figure P6.58



SOLUTION:

6.59 Given a 1-, 3-, and 4-μF capacitor, can they be interconnected to obtain an equivalent 2-μF capacitor?



SOLUTION:

6.60 Select the value of C to produce the desired total capacitance of C T = 10 μF in the circuit in Fig. P6.60.

8 μF 16 μF

C

CT = 10 μF

Figure P6.60



SOLUTION:

6.61 Select the value of C to produce the desired total capacitance of C T = 1 μF in the circuit in Fig. P6.61.

1 μF

1 μF

1 μF2 μF

CC

CT

Figure P6.61



SOLUTION:

6.62 The three capacitors shown in Fig. P6.62 have been connected for some time and have reached their present values. Find V 1 and V 2 .

V1

V2

8 μF

4 μF

12 V

+

−

+

−

+

−

Figure P6.62



SOLUTION:

6.63 The two capacitors in Fig. P6.63 were charged and then connected as shown. Determine the equivalent capacitance, the initial voltage at the terminals, and the total energy stored in the network.

2 V

6 V 12 μF

4 μF

−

+

+

−

Figure P6.63



SOLUTION:

6.64 The two capacitors shown in Fig. P6.64 have been connected for some time and have reached their present values. Find V o .

16 V

Vo 12 μF

4 μF

+

−

+

−

Figure P6.64



SOLUTION:

6.65 Determine the inductance at terminals A-B in the network in Fig. P6.65.

A

B2 mH

3 mH 4 mH

1 mH

2 mH12 mH4 mH

Figure P6.65



SOLUTION:

6.66 Find the total inductance, L T , in the network in Fig. P6.66. All inductors are in millihenrys.

LT

2 4

1

3

12

18 5

6

Figure P6.66



SOLUTION:


8

6

9

184

3

9

LT

Figure P6.67



SOLUTION:


LT

12 4

6

2

1

2

31

Figure P6.68



SOLUTION:

6.69 Find the total inductance L T in the network in Fig. P6.69. All inductors are in millihenrys.

LT

12 4

9

6

2

1

2

3

Figure P6.69



SOLUTION:

6.70 Find the total inductance at the terminals of the network in Fig. P6.70.

12 mH

6 mH

2 mH4 mHLT

12 mH

Figure P6.70



SOLUTION:

6.71 Find L T in the circuit in Fig. P6.71.

LT

4 μH

12 μH

5 μH 2 μH

6 μH

3 μH

Figure P6.71



SOLUTION:

6.72 Find L T in the network in Fig. P6.72 (a) with the switch open and (b) with the switch closed. All inductors are 12 mH.

LT

Figure P6.72



SOLUTION:

6.73 Determine the inductance at terminals A-B in the network in Fig. P6.73.

A

B1 mH 2 mH

1 mH 1 mH

4 mH

2 mH

2 mH

12 mH

6 mH

Figure P6.73



SOLUTION:

6.74 Compute the equivalent inductance of the network in Fig. P6.74 if all inductors are 4 mH.

Leq

Figure P6.74



SOLUTION:

6.75 Find the value of L in the network in Fig. P6.75 so that the value of L T will be 2 mH.

4 mH

1 mH

2 mH

6 mHLT

LL

Figure P6.75



SOLUTION:

6.76 Find L T in the circuit in Fig. P6.76. All inductors are 12 μH.

LT

Figure P6.76



SOLUTION:

6.77 Find the total inductance, L T , in the network in Fig. P6.77. All inductors are 6 millihenrys.

LT

Figure P6.77



SOLUTION:


LT

5 μH

8 μH

12 μH 6 μH

6 μH

12 μH

2 μH1 μH

4 μH

4 μH

Figure P6.78



SOLUTION:


LT

2 μH

9 μH 3 μH 12 μH

6 μH

4 μH 6 μH 4 μH

8 μH 4 μH

12 μH

3 μH

Figure P6.79



SOLUTION:

6.80 If the total inductance, L T , of the network in Fig. P6.80 is 6 μH, find the value of L.

LT = 4 μHL

2 μH 8 μH

18 μH 9 μH3 μH

4 μH

4 μH

1 μH

Figure P6.80



SOLUTION:

6.81 Given the network shown in Fig. P6.81, find (a) the equivalent inductance at terminals A-B with terminals C-D short circuited, and (b) the equivalent inductance at terminals C-D with terminals A-B open circuited.

12 mH5 mH

20 mHA C

B D6 mH

Figure P6.81



SOLUTION:

6.82 Find the value of L in the network in Fig. P6.82 so that the total inductance, LT, will be 2 mH.

4 mH

L

2 mH

6 mH

LT

Figure P6.82



SOLUTION:

6.83 A 20-mH inductor and a 12-mH inductor are connected in series with a 1-A current source. Find (a) the equivalent inductance and (b) the total energy stored.

Ch06 Solution

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