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Power Calculations 1. Some of the elements in the circuit below supply power to the circuit and others receive
power from the circuit. Unlike a resistor, sources such as a battery do not necessarily dissipate the power that they receive (e.g. a rechargeable battery will store it as energy through a reversible chemical reaction, though some power will be dissipated as this process is never 100% efficient). Find the power supplied/received by each source.
60 V
2 A 80 V
5 A
100 V
Answer: Source Power Received
or Supplied?
2A 320.W Received 60V 120.W Supplied 80V 400.W Received 5A 900.W Supplied 100V 300.W Received
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2. If the connection is valid, find the total power developed in the circuit.
50 V
30 I80 V
5 A
200 VI
2 A
Total Power delivered = 1.00kW
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3. The following circuit satisfies Kirchhoff's Laws. If V0=100V, find the total power received
by all of the circuit elements that are receiving power from the rest of the circuit.
4 A
I
ig
60 V
80 V
2 I+v0-
Total Power received = 2.24 kW
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4. Calculate the power being supplied to the rest of the circuit by the dependent source.
6
0.9Ix
ix
3
6
15 9 6 A 4 A
6
0.9Ix
ix
3
6
15 9 6 A 4 A
Dependent source power = 30.0 W supplied
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5. Calculate the total power supplied and received by each element in the circuit below. Clearly state whether each element is supplying or receiving power.
20 V 20
5I2
V1/4 5
I2+
v1
-
I1 I3
I4+
Vx
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Element Voltage Current Power Is power supplied or
receiving? 20 V source 20 resistor Dependent source 5i2
Dependent source v1/4
5 resistor Answers: Element Voltage Current Power Is power supplied or
absorbed? 20 V source V1 = 20.0 V I1 = 9.00 A - 180. W 180. W supplied 20 resistor V1 = 20.0 V I2 = 1.00 A 20.0 W 20.0 W receiving Dependent source 5i2 5.00 V I3 = 8.00 A 40.0 W 40.0 W receiving Dependent source v1/4 Vx = 15V 5.00 A 75.0 W 75.0 W receiving 5 resistor Vx = 15V I4 = 3.00 A 45.0 W 45.0 W receiving
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Design Problems 6. Find R1 and R2 such that V0 = 5V and the power dissipated in R1 is 0.25W.
25 V
150
R2
R1
R1+
V0
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R1 = 100. R2 = 200.
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7. The circuit below is a voltage divider circuit designed to produce three voltages for use in other circuits. Calculate R1, R2, and R3 in order to produce no-load voltages of 12V, 6V, and -12V and under the constraint that the total power dissipated is 36W.
24 V R2
R1
R3
R1 = 4.00 R2 = 4.00 R3 = 8.00
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8. Specify the resistors in the following circuit to meet the following design criteria: Ig = 8 mA, Vg = 4 V, I1 = 2I2, I2=10I3, and I3=I4.
Ig R1 R2 R4R3
I2I1 I3 I4
+
Vg
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R1 = 800. R2 = 1.60 k R3 = 16.0 k R4 = 16.0 k
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9. All of the resistors in the circuit below have the same value R. a. Find the value of R such that the source provides 1.0W of power to the circuit. b. If all of the resistors are to have the same power rating, what is the minimum power
rating required to avoid exceeding the maximum? Assume the power rating may change by 1/8W increments (eg. 1/8W, 1/4W, 3/8W, etc.). (Hint: identify the resistor that dissipates the most power and compute its power rating requirements.)
0.100A
R
R
R
R
R R
R
R
R
R
a. R = 0.100 k b. Min power rating = W
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Resistors in Series and Parallel 10. Determine which elements in the circuit below are in series and which elements are in
parallel.
Series: 5, 6, 7 Parallel: 8||4, 1||3, 2||9
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11. Calculate the equivalent resistance Rab.
5 15 20
10 16 66
40 50 60
55
Rab
Rab = 35.0
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12. Calculate the equivalent resistance Rab.
2.5 6 5
3.4 11.25 10
26 75
20
60
Rab
3
15
Rab =15.0
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13. Calculate the equivalent resistance Rab.
45
15
6 1.5
1
40 5
5.2
3
12Rab
Rab =10.0
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14. Calculate the equivalent resistance Rab.
125 34 15
50 3.33 13
50 50
80
60
Rab15200
Rab =0.100 k
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Conceptual Problems 15. For the following problem, assume the values are accurate to two significant figures. For the circuit shown below:
a. For both switches open, what are VA and VB? b. For both switches closed, what are VA and VB? c. For switch A open, and switch B closed, what are VA and VB? d. For switch B open and switch A closed, what are VA and VB?
12.8.0 V
Sw A
Sw B15.
+ V A -+
V B
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Question VA VB a -8.0 V 0.0 V b 0.0 V 0.0 V c -8.0 V 0.0 V d 0.0 V -4.4 V
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16. The circuit below consists of light bulbs A and B, switches I and II, an ideal voltage source V1, and a variable resistor R1. Fill in the blanks below, using these possible responses.
1) Both light bulbs are off
2) Light bulb A is on, light bulb B is off 3) Light bulb A is off, light bulb B is on
4) Both light bulbs are on and light bulb A is brighter
5) Both light bulbs are on and light bulb B is brighter
6) Both light bulbs are on and they have the same intensity
___ Both switches are open ___ Switch I is closed, switch II is open ___ Switch I is open, switch II is closed ___ Both switches are closed 17. Resistor R is increased in the circuit below. What happens to:
a. The power dissipated in R? b. The power dissipated in R1? c. The power dissipated in R2? d. The power supplied by Vs?
Vs R1 R2R
III
A B
III
A B
Answers: 2 Both switches are open 4 Switch I is closed, switch II is open 6 Switch I is open, switch II is closed 6 Both switches are closed
Answers: a. Power dissipated in R decreases. b. No change c. No change d. Power supplied by Vs decreases.
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18. The circuit below has four identical light bulbs connected to an ideal battery.
a. How do the brightness of these bulbs compare? Assume brightness is directly related to power.
b. Which light bulb(s) draws the least amount of current?
c. What happens to the brightness of the remaining light bulbs when light bulb C is removed?
d. What happens to the brightness of the remaining light bulbs when light bulb D is removed
19. Resistor R is decreased in the circuit below. What happens to:
a. The power dissipated in R? b. The power dissipated in R1? c. The power dissipated in R2? d. The power supplied by Is? Is
R1 R2
R
A B
C
D
A B
C
D
Answers:
a. (A&D) > (B&C) b. B&C c. A&D decrease; B increases d. They all go out
Answers: a. Power in R decreases b. No change c. No change d. Power supplies by Is decreases
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Analysis 20. Use voltage division and the circuit below to complete the table shown.
VR1 R2
R3
+ V1 - + V2 -
+V3-
V R1 V1 R2 V2 R3 V3
(a) 6 V 1 2 3
(b) 2 4 0.5 1 V
(c) 5 V 3 V 1 V 5
(d) 2.5 V 1.5 0.5 V 2.5 Answers
V R1 V1 R2 V2 R3 V3
(a) 6 V 1 1.00 V 2 2.00 V 3 3.00 V
(b) 13.0 V 2 4.00 V 4 8.00 V 0.5 1 V
(c) 5 V 15.0 3 V 5.00 1 V 5 1.00 V
(d) 2.5 V 1.5 0.5 V 2.5 0.833 V 3.50 1.17 V
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21. Use current division and the circuit below to complete the table shown.
R1 R2I R3
I1 I2 I3
I R1 I1 R2 I2 R3 I3
(a) 1.5 A 3 6 30
(b) 2 A 1 A 10 40
(c) 8 8 20 1 A
(d) 3 A 1 A 10 1 A Answers:
I R1 I1 R2 I2 R3 I3
(a) 1.5 A 3 0.938 A 6 0.469 A 30 0.094 A
(b) 2 A 8.00 1 A 10 0.800 A 40 0.200 A
(c) 6.00 A 8 2.50 A 8 2.50 A 20 1 A
(d) 3 A 10.0 1 A 10.0 1.00 A 10 1 A
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22. Find Vg and the power dissipated in the 20 resistor given that 1 A of current flows in the 9 resistor.
20
Vg
10 5 4
3 1
32 25 9 40 2
1 A
P20 = 28.8W Vg = 144. W
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23. For the following circuit: a. Given that I0 = 0.54A, find Ix. b. Find Ix if the 20 resistor is changed to 10 .
Ix
60 10 48 15
10
20
18
8 6
30
I0
Answers: a. Ix = 6.00 A b. Ix = 5.40 A
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24. Find Vo in the following circuit:
18 mA
10 k
12 k15 k
3 k
2 k 4 k+ Vo -
Answer: Vo = 33.8 V
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25. Find Vo and Vg in the following circuit:
25 A
12 50 30
30 60
25
+
Vg
- +
Vo
-
Answers: Vo = 0.300 kV Vg = 1.05 kV
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26. Find Io and Ig in the following circuit:
125 V
2
6
20
13
12
5
15
Ig
Io
Answers: Io = 2.00 A Ig = 12.5 A
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27. In the following circuit, the no-load value of Vo = 6 V. When RL is connected, Vo drops to 4V. Find the value of RL.
18V
40
R2 RL
+
Vo
-
Answer: RL = 26.7
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28. Calculate Io and the power dissipated in the 10 resistor.
75 V
4 3
10 30 40
Io
Answers: Io = -1.00 A P10 = 160. W
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29. Find the current, voltage and power associated with the 20 k resistor.
5 mA 10 k 0.01 Vo5 k 20 k
+
Vo
_
+
V1
-
I1
Answers: V1 = 2.00 kV I1 = 100. mA P20k = 200. W
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30. The following represents a two-stage amplifier which converts an input signal to a larger output signal.
a. Calculate Iout and Vout. b. Calculate the voltage gain which is defined as Vout/Vin.
Vin = 10V4 V1
4.5 I2
2
6 3 6
5
10
+
V1
-
I2
+
Vout
-
Iout
Answers: a. Vout = 30.0 V, Iout = 3.00 A b. Voltage Gain = 3.00
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31. Calculate Vx and Ix in the circuit below.
2.00 A
2Vx
1.00
3.00
+
Vx
-
Ix
Vx = -0.600 V Ix = 1.80 A
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32. In the circuit below, calculate values for vx and V1.
-
12 mA
+ +
-
-3 mAV1
10 k 1 k
vx
1 mA
3.5 mA
0.03vx-
12 mA
+ +
-
-3 mAV1
10 k 1 k
vx
1 mA
3.5 mA
0.03vx
Answers: Vx = -2.00 V V1 = -515. V
