Introductory Circuit Analysis, Tenth Edition...Introductory Circuit Analysis, Tenth Edition Author Robert L. Boylestad Keywords Introductory Circuit Analysis, Tenth Edition Robert

160 SERIES CIRCUITS S

R

10 � 12 �

(a)

RT = 30 �I

30 V

50 � 60 �

(c)

RT = 220 �

I

120 V

R1

10 �R2 = R1

12.6 k� R

(b)

RT = 60 k�

I

60 V

45 k� 0.4 k�

0.2 M�

(d)

RT = 1.6 M�

50 V

E

100 k�

R

56 k�

I

PROBLEMS

SECTION 5.2 Series Circuits

1. Find the total resistance and current I for each circuit ofFig. 5.71.

2. For the circuits of Fig. 5.72, the total resistance is speci-fied. Find the unknown resistances and the current I foreach circuit.

FIG. 5.72

Problem 2.

2 �

RT

6 � 12 �I

15 �I

E = 60 V

E = 35 V 25 � 25 �10 �

25 � 10 �

200 k�

RT

1 M�

0.1 M�

E

I

10 V 330 k�

1.2 k�

RT

3 k� 1.3 k�

I

E = 120 V 4.5 k�

2.2 k�

(b)

(d)

(a)

(c)

RT

FIG. 5.71

Problems 1 and 36.

PROBLEMS 161S

(a)

I = 4 mA

60 �

E

1.2 k�

2.74 k�

(b)

I = 250 mA

8.2 �

E

1.2 �

2.7 �

4.7 �

FIG. 5.73

Problem 3.

FIG. 5.75

Problem 5.

FIG. 5.74

Problem 4.

2 �E

5 �

R

I

(a)

12 V

+

–RT = 16 �

2.2 k�3.3 k�

RI

(b)

P = 79.2 mW

– 9 V +

E

*4. For each network of Fig. 5.74, determine the current I,the source voltage E, the unknown resistance, and thevoltage across each element.

SECTION 5.3 Voltage Sources in Series

5. Determine the current I and its direction for each networkof Fig. 5.75. Before solving for I, redraw each networkwith a single voltage source.

3. Find the applied voltage E necessary to develop the cur-rent specified in each network of Fig. 5.73.

4.7 �

(a)

16 V

8 V

5.6 �

I

1.2 �

4.7 �

(b)

18 V

4 V

10 V5.6 �

I

4 V

162 SERIES CIRCUITS S

FIG. 5.76

Problem 6.

E 5 k�

P = 100 mW

RI = 5 mA

20 V+ –

(a)

+–

16 V 2 k�

+

–

+– +–6 V 12 V

8 V–

+

+–E

(b)

R

–

10 V

2 V

3 V

V ab

b a

+

–

+

–

+ –

60 V

20 V

10 Vb

+

–

+

– +

R

aV ab

Opencircuit

(a) (b)

FIG. 5.77

Problem 7.

6 V

10 VV2 –

++

–V1

+ –

+

–

(a)

24 V

10 V 6 V

2.2 k�V1 R1

+

–

(b)

V2+ –

R2 = 5.6 k�

FIG. 5.78

Problem 8.

*6. Find the unknown voltage source and resistor for the net-works of Fig. 5.76. Also indicate the direction of theresulting current.

SECTION 5.4 Kirchhoff’s Voltage Law

7. Find Vab with polarity for the circuits of Fig. 5.77. Eachbox can contain a load or a power supply, or a combina-tion of both.

8. Although the networks of Fig. 5.78 are not simply seriescircuits, determine the unknown voltages using Kirch-hoff’s voltage law.

PROBLEMS 163S

0.56 k�

9 V

27 V

2.2 k�

I5 V

V1+ –

1.2 k�

FIG. 5.79

Problem 9.

120 V

1 k�

I V2+ –

2 k�

V3+ –

3 k�

V1+ –

RT

FIG. 5.80

Problem 10.

9. Determine the current I and the voltage V1 for the net-work of Fig. 5.79.

10. For the circuit of Fig. 5.80:a. Find the total resistance, current, and unknown volt-

age drops.b. Verify Kirchhoff’s voltage law around the closed

loop.c. Find the power dissipated by each resistor, and note

whether the power delivered is equal to the power dis-sipated.

d. If the resistors are available with wattage ratings of1/2, 1, and 2 W, what minimum wattage rating can beused for each resistor in this circuit?

11. Repeat Problem 10 for the circuit of Fig. 5.81.

*12. Find the unknown quantities in the circuits of Fig. 5.82using the information provided.

13. Eight holiday lights are connected in series as shown inFig. 5.83.a. If the set is connected to a 120-V source, what is the

current through the bulbs if each bulb has an internalresistance of 28�

18

� �?b. Determine the power delivered to each bulb.c. Calculate the voltage drop across each bulb.d. If one bulb burns out (that is, the filament opens),

what is the effect on the remaining bulbs?

+

22 �RT

I

V1–

10 �

5.6 �

33 �

+V4– +V3–

+V2

–6 V

FIG. 5.81

Problem 11.

FIG. 5.83

Problem 13.

20 � R

I

1 �

120 V

2.2 �

E

4.7 �

6.8 �+V2

–

2 � P = 21 W1 A +

V3–

RE

P = 4 WI

E

RT = 16 �

P = 8 W

R1 R2

1 �

(a) (b)

(c) (d)

I

+ V – + 80 V – – 8 V + – V1 +

+ V1 – + V2 –

FIG. 5.82

Problem 12.

164 SERIES CIRCUITS S

R = ?E

R1

2 �

24 V

24 W

4 �

R2

FIG. 5.84

Problem 14.

FIG. 5.85

Problems 15 and 37.

50 �

a

b

25 �

100 V

(a)

Vab

2 k�

a

b

4 k�

40 V

(c)

Vab

3 k�

1 k�

a

b

2.5 �

0.36 V

(d)

0.6 �

1.5 �

0.5 � 0.9 �

Vab

80 V

(b)

6 �

20 � 4 �

Vab

10 � a b

*14. For the conditions specified in Fig. 5.84, determine theunknown resistance.

2 k�

20 V

(a)

4 V

6 k�

R

+

–

R

200 V

(b)

3 �

+

–

6 �V = 140 V

FIG. 5.86

Problem 16.

SECTION 5.6 Voltage Divider Rule

15. Using the voltage divider rule, find Vab (with polarity) forthe circuits of Fig. 5.85.

16. Find the unknown resistance using the voltage dividerrule and the information provided for the circuits of Fig.5.86.

PROBLEMS 165S

R1 10 �

R2 30 �

R3 V3

+

–

V2

+

–

4 V

+

–

I

40 V

FIG. 5.87

Problem 17.

17. Referring to Fig. 5.87:a. Determine V2 by simply noting that R2 � 3R1.b. Calculate V3.c. Noting the magnitude of V3 compared to V2 or V1,

determine R3 by inspection.d. Calculate the source current I.e. Calculate the resistance R3 using Ohm’s law, and

compare it to the result of part (c).

18. Given the information appearing in Fig. 5.88, find thelevel of resistance for R1 and R3.

19. a. Design a voltage divider circuit that will permit theuse of an 8-V, 50-mA bulb in an automobile with a12-V electrical system.

b. What is the minimum wattage rating of the chosenresistor if 1⁄4-W, 1⁄2-W and 1-W resistors are available?

20. Determine the values of R1, R2, R3, and R4 for the voltagedivider of Fig. 5.89 if the source current is 16 mA.

21. Design the voltage divider of Fig. 5.90 such that VR1�

(1/5)VR2if I � 4 mA.

22. Find the voltage across each resistor of Fig. 5.91 if R1 �2R3 and R2 � 7R3.

23. a. Design the circuit of Fig. 5.92 such that VR2� 3VR1

and VR3� 4VR2

.

b. If the current I is reduced to 10 mA, what are the newvalues of R1, R2, and R3? How do they compare to theresults of part (a)?

FIG. 5.88

Problem 18.

R1

+12 V

R2 8 �

R3

+4 V

–4 V

–8 V

R1

R2

+48 V

R3

R4

+12 V

–20 V

16 mA

100 VE

FIG. 5.89

Problem 20.

FIG. 5.90

Problem 21.

R1 R2I

–+ 72 V

FIG. 5.91

Problem 22.

R2 V2

+

–

R3 V3

+

–

R1 V1

+

–

60 V

FIG. 5.92

Problem 23.

R1 R2

R3

+64 VE

–

I = 10 mA

166 SERIES CIRCUITS S

SECTION 5.7 Notation

24. Determine the voltages Va, Vb, and Vab for the networksof Fig. 5.93.

FIG. 5.93

Problem 24.

(a)

8 V

VbVa

12 V

(b)

4 V

VbVa

6 V20 V

(c)

Vb+ 10 V

3 V 8 V

Va

21 V

25. Determine the current I (with direction) and the voltage V(with polarity) for the networks of Fig. 5.94.

FIG. 5.94

Problem 25.

I

6 � 3 � V

120 V 60 V

I

30 �

–10 V

–70 V

20 �

10 �

V(a) (b)

26. Determine the voltages Va and V1 for the networks ofFig. 5.95.

V120 �V1

2.2 k�

(a)

Va8 V

(b)

+ 12 V10 V

Va+ –

3.3 k�

– 8 V10 � +

–16 V

FIG. 5.95

Problem 26.

*27. For the network of Fig. 5.96, determine the voltages:a. Va, Vb, Vc, Vd, Ve

b. Vab, Vdc, Vcb

c. Vac, Vdb

FIG. 5.96

Problem 27.

4 k�

b47 V2 k�

20 V

a3 k�

c d

e

PROBLEMS 167S

*29. For the integrated circuit of Fig. 5.98, determine V0, V4,V7, V10, V23, V30, V67, V56, and I (magnitude and direc-tion).

FIG. 5.98

Problem 29.

6 mA

2 k�

4 �

–8 V

–2 V

20 V

12

43 65

70

–2 V

4 V

I

*28. For the network of Fig. 5.97, determine the voltages:a. Va, Vb, Vc, Vd

b. Vab, Vcb, Vcd

c. Vad, Vca 4 k�

2 k�ab

c

6 k�

44 V

20 V

d

FIG. 5.97

Problem 28.

*30. For the integrated circuit of Fig. 5.99, determine V0, V03,V2, V23, V12, and Ii.

3 k�E

2 mA

3

21

0

20 V

Ii

1 k�5 mA

10 mA

FIG. 5.99

Problem 30.

VL 3.3 �

+

–

Rint = 0.05 �

E = 12 V

FIG. 5.100

Problems 32 and 35.

SECTION 5.8 Internal Resistance of Voltage Sources

31. Find the internal resistance of a battery that has a no-loadoutput voltage of 60 V and that supplies a current of 2 Ato a load of 28 �.

32. Find the voltage VL and the power loss in the internalresistance for the configuration of Fig. 5.100.

33. Find the internal resistance of a battery that has a no-loadoutput voltage of 6 V and supplies a current of 10 mA toa load of 1/2 k�.

SECTION 5.9 Voltage Regulation

34. Determine the voltage regulation for the battery of Prob-lem 31.

35. Calculate the voltage regulation for the supply of Fig.5.100.