Determine the maximum average power that may be absorbed
by a load attached to terminals a–b of this network.
Spring 2014, Exam #1, Problem #3
Answer: 20 W
1
The voltage across and current through an element are given by the following waveforms:
i  t   2cos 10 t   4  mA
v  t   100 cos 10 t   4  μV
(a) Calculate the instantaneous power absorbed by this element at t = 0 .
(b) Determine the average power absorbed by this element over 1 sinusoidal period.
Spring 2014, Exam #1, Problem #1(a),(d)
Answers: (a) 314 nW , (b) 0 W
2
The plot below shows one full cycle of a periodic current waveform.
Calculate the effective (RMS) value of this waveform.
Spring 2014, Exam #1, Problem #2(b)
Answer: 2 mARMS
3
For the circuit shown, choose an element or network (including component values) which,
when placed at a–b, corrects the power factor at the voltage source to 1 and
does not absorb additional power.
Spring 2014, Exam #1, Problem #4
Answer: capacitor, 10 mF
4
In the circuit below, determine the average power absorbed
by the independent current source.
Spring 2015, Exam #2, Problem #1
Answer: –27 W
5
A voltage source is connected to a load as shown. The load absorbs 346.4 W of average
power at VL = 80 VRMS with a power factor of 0.866 . The source frequency is 5 rad/s.
Determine the type and value of a single element to be placed in parallel with the load
so that the power factor at the new load is 1.
Spring 2015, Exam #2, Problem #2
Answer: 6.25 mF
6
Determine the effective (RMS) value of the periodic voltage waveform in the figure.
Spring 2015, Exam #1, Problem #3(a)
Answer: 8 VRMS
7
Determine the coil voltage v4(t) .
Spring 2015, Exam #1, Problem #3(b)
Answer: 20cos  2t  143 V
8
In the circuit below, determine V2 for n = 3 .
Spring 2015, Exam #1, Problem #4
Answer: 3620 V
9
Write a valid matrix equation whose solution contains the values for I1 , I2 , and I3 .
Let  = 2 rad/s.
Spring 2014, Exam #2, Problem #2
2 j
4 j   I1   0 
7  4 j

   
Answer:
 4 j 11  6 j 24  10 j  I 2    0 
 2 j
11  8 j 11  6 j   I 3   9
10
For the circuit below, determine vo(t).
Spring 2014, Exam #2, Problem #3
Answer: 6cos  5t  165 V
11
For the network below, determine the Thevenin equivalent at terminals a–b.
Spring 2014, Exam #2, Problem #4
Answer: 4 
12
The waveform shown is the current through the load impedance 1260  .
Calculate the average power absorbed by this load for Im = 8 A , T = 5 s .
Spring 2015, Final exam, Problem #3
Answer: 128 W
13
The source voltage is Vs  12075 VRMS . The load impedance is Z L  20  j 20  .
Choose a circuit element, including its value, which corrects the power factor of the parallel
combination (seen by the source) to unity and does not absorb additional power.
The operating frequency is 100 rad/s.
Spring 2015, Final exam, Problem #4
Answer: capacitor, 250 F
14
Determine the power absorbed at t = 1.5 ms by each of the three elements in the circuit shown
below if vs is equal to (a) 30u(–t) V , (b) 10 + 20u(t) V .
Spring 2014, Homework #3, Problem #1
Answers: (a) ps = 0 W , pR = 401.6 W , pC = –401.6 W ,
(b) ps = –566.8 mW , pR = 178.5 mW , pC = 388.3 mW
15
Assuming no transients are present, calculate the power absorbed by the current source in the
circuit below at (a) t = 0 , (b) t = 10 ms , (c) t = 20 ms .
Spring 2014, Homework #3, Problem #2
Answers: (a) –6.25 W , (b) –6.19 W , (c) –6.00 W
16
Calculate the total average power absorbed by the passive elements in the circuit below.
Spring 2014, Homework #3, Problem #3
Answer: 5.29 kW
17
(a) Calculate the average power supplied to each passive element in the circuit below.
(b) Determine the power supplied by each source.
(c) Replace the 8- resistive load with an impedance capable of drawing
maximum average power from the remainder of the circuit.
Spring 2014, Homework #3, Problem #4
Answers: (a) p4.8 = 69.6 W , p8 = 36 W , pL = 0 , (b) pIS = –9.6 W , pDS = –96 W ,
(c) –8 + j3.2 
18
Compute the effective value of
(a) i(t) = 3sin(4t) A
(b) v(t) = 4sin(20t)cos(10t) V
(c) i(t) = 2 – sin(10t) mA
(d) the waveform plotted below.
Spring 2014, Homework #3, Problem #5
Answers: (a) 2.12 ARMS , (b) 0.5 VRMS , (c) 2.12 ARMS , (d) 2.3 mARMS
19
For the circuit below, find the apparent power delivered to each load,
and the power factor at which the source operates, if
Z A  5  2 j  , ZB  3  , ZC  8  4 j  , ZD  15  30  .
Spring 2014, Homework #3, Problem #6
Answers: APA = 3.4 kVA , APB = 1.64 kVA , APC = 95.8 VA , APD = 160.6 VA ,
PF = 0.977 leading
20
Determine the value of capacitance that must be added in parallel to the 10- resistor in the
circuit below in order to increase the power factor of the source to 0.95 at 50 Hz.
Spring 2014, Homework #3, Problem #7
Answer: 361 F
21
With respect to the circuit depicted below, calculate (a) the voltages v1 and v2 , and (b) the
average power delivered to each resistor.
Spring 2014, Homework #5, Problem #2
Answers: (a) –685 mV , –1.58 V ,
(b) p2.7 = 759 mW , p2 = 562 W , p4 = 28.2 mW , p100 = 12.5 mW
22
Determine the Thevenin equivalent of the network below as seen looking into terminals a and b .
Spring 2014, Homework #5, Problem #3
Answer: –931 m
23
Find the average power delivered to each element for the circuit below.
Spring 2015, Homework #3, Problem #1
Answers: p10 = 625 W , pCS = –1000 W , p15 = 937.5 W , pVS = –562.5 W , pC = 0 W
24
Determine the root-mean-square (RMS) value for each of the waveforms below.
(a)
(b)
Spring 2015, Homework #3, Problem #2
Answers: (a) 2.05 VRMS , (b) 8.3 VRMS
25
The circuit below consists of a source connected to a load.
(a) Suppose R = 9  and L = 5 H. Determine the average, complex, and reactive powers
delivered by the source to the load.
(b) Suppose R = 15  and L = 3 H. Determine the average, complex, and reactive powers
delivered by the source to the load.
(c) Suppose the source delivers 8.47 + j14.12 VA to the load. Determine the values of the
resistance R and the inductance L.
(d) Suppose the source delivers 14.12 + j8.47 VA to the load. Determine the values of the
resistance R and the inductance L.
Spring 2015, Homework #3, Problem #3
Answers: (a) S = 8.47 + j14.1 VA , (b) S = 14.1 + j8.47 VA , (c) 9  , 5 H , (d) 15  , 3 H
26
A voltage source with a complex internal impedance is connected to a load, as shown below.
The load absorbs 1 kW of average power at 100 VRMS with a power factor of 0.80 lagging. The
source frequency is 200 rad/s. (a) Determine the source voltage V1 . (b) Find the type and
value of the element to be placed in parallel with the load so that maximum power is transferred
to the load.
Spring 2015, Homework #3, Problem #4
Answers: (a) 200 VRMS , (b) 750 F
27
Determine the complex power supplied by the source in the circuit shown below.
Spring 2015, Homework #3, Problem #6
Answer: 219.2 + j111.2 VA
28
Find V1 and I1 for the circuit below when n = 5 .
Spring 2015, Homework #3, Problem #7
Answers: V1 = 8 – j6 V , I1 = 2 A
29
In the circuit below, is  8  7u  t  A .
Determine the instantaneous power absorbed by the capacitor as a function of time.
Spring 2016, Homework #3, Problem #1
Answer: 42et 60 m  294et 30 m W
30
In the circuit below, determine the average power absorbed by the current source.
Spring 2016, Homework #3, Problem #2
Answer: –21 mW
31
Determine the root-mean-square (RMS) value of each waveform.
(a)
(b)
Spring 2016, Homework #3, Problem #3
Answers: (a) 0.33 VRMS , (b) 1.22 VRMS
32
In the circuit below, the load is 1000 + j900  .
Determine the power factor at which the current source is operating.
Spring 2016, Homework #3, Problem #4
Answer: 0.95
33
In the circuit below, the motor draws a complex power equal to 15024 kVA . The source
voltage is 230 VRMS . Determine the impedance of the purely reactive corrective device required
to achieve a power factor of 0.98 at the source (open terminals).
Spring 2016, Homework #3, Problem #5
Answer: –j1.6 
34
In the circuit below, determine the voltage v(t) .
Spring 2016, Homework #3, Problem #6
Answer: 6cos  2t  90 V
35
In the circuit below, determine the steady-state current i2(t) .
Spring 2016, Homework #9, Problem #3
Answer: 130cos  25t  64 mA
36
In the circuit below, determine the Thevenin equivalent voltage (as a function of time) of this
network with respect to terminals C–D.
Spring 2016, Homework #9, Problem #4
Answer: 12cos  3t  V
37
Determine the effective value of v(t) as drawn in the figure.
Spring 2016, Homework #9, Problem #5
Answer: 8.5 VRMS
38
A motor is powered by a single-phase, 480-VRMS , 60-Hz voltage source.
The motor absorbs a real power of 7460 W.
Uncorrected, the motor has a power factor of 0.93 lagging.
The motor’s power factor must be corrected to 0.99 lagging.
The correction will be accomplished by adding a component in parallel with the motor.
The component must not absorb additional real power.
Determine the type of the component (resistor, capacitor, inductor)
and the proper size of the component (Ω, F, H) to accomplish this goal.
Spring 2016, Exam #2, Problem #1
Answers: capacitor, 22 F
39
In the circuit given, a and L are set so that maximum power is absorbed by the load (the 200-
resistor and inductor in series). Determine the value of the inductance L .
Spring 2016, Exam #2, Problem #2
Answer: 500 mH
40
For the linear-transformer circuit given, determine the steady-state current i(t) .
Spring 2016, Final exam, Problem #4
Answer: 5cos 10t  80 mA
41
For the circuit given, determine…
(a) the Thevenin equivalent impedance at terminals A-B in rectangular form, and
(b) the maximum amount of power that may be absorbed from this network
by a load placed across terminals A-B.
Spring 2016, Final exam, Problem #1
Answers: (a) 18  j963  , (b) 7.2 mW
42