MINISTRY OF SCIENCE AND TECHNOLOGY
DEPARTMENT OF
TECHNICAL AND VOCATIONAL EDUCATION
SAMPLE QUESTIONS & WORKED OUT
EXAMPLE
For
EP-02011
ELECTRICAL ENGINEERING CIRCUIT ANALYSIS II
A.G.T.I YEAR II
ELECTRICAL POWER ENGINEERING
-1-
EP 02011, ELECTRICAL ENGINEERING CIRCUIT ANALYSIS II
SAMPLE QUESTIONS
CHAPTER 1
UNITS, DEFINITIONS, EXPERIMENTAL LAWS, AND SIMPLE CIRCUITS
1*.
Determine ix and vx in each of the following circuits:
18 V
RA
12 A
5A
5Ω
8Ω
vx
6Ω
ix
4Ω
10Ω
60 V
(a)
2*.
2Ω v x
ix
(b)
(a) Find the voltage, current, and power associated with each element in the
following circuit.
12 0A
30 A
30 S
15 S
(b) Determine the values of v and power absorbed by the independent current
source.
ix
6kΩ
3*.
2i x
v
24mA
2kΩ
What is the correct reading of an ohmmeter if this instrument is attached to the
-2network of the following figure at points: (a) ac;(b) ab;(c) cd?
50Ω
25Ω
b
16Ω
30Ω
c
15Ω
4*.
7Ω
a
4Ω
d
12Ω
In the following circuit: (a) use resistance combination methods to find Req; (b)
use current division to find i1; I find i2; (d) find v3.
i1
2Ω
40Ω
i2
12 0mA
5**.
125Ω
50Ω
240Ω
R eq
20Ω
v3
Determine Gin for each network shown in the following Figures. Values are all
given in millisiemens.
Gin
0.8
5
50
3
2.5
4
Gin
2
0.5
100
40
6
1.5
25
( a)
6**.
30
(b)
Use current and voltage division on the following circuit to find an expression for
(a) v2; (b) v1; (c) i4.
R3
R1
i4
v1
VS
7**.
R2
v2
R4
(a) Let vx = 10 V and find Is; (b) let Is = 50 A and find vx; (c) calculate
-3the ratio vx/Is.
2Ω
IS
1Ω
4Ω
5Ω v X
3Ω
8***. Use current and voltage division to obtain an expression for v5.
R2
VS
R1
R4
R5
R3
v5
9***. Find the power absorbed by each source of the following Figure. To what
value should the 4 V source be changed to reduce the power
supplied by the -5 A source to zero?
-5 A
2V
3A
-4 A
4V
************************
12 A
-3 V
-4CHAPTER 2
SOME USEFUL TECHNIQUES OF CIRCUIT ANALYSIS
1*.
Determine the values of the unknown node-to-reference voltages in the following
circuit.
v2
2Ω
vX
0.5Ω
14 A
0.5v X
12 V
Ref
v1
vy
2.5Ω
1Ω
v3
0.2v y
v4
2*.
Use mesh analysis to determine the three unknown mesh currents in the following
circuit.
1Ω
7V
i1
i2
3Ω
6V
i3
2Ω
3*.
2Ω
1Ω
Apply superposition to the following circuit and find i3.
30 Ω
8A
50Ω
30 Ω
i3
100 V
60Ω
60 V
-5-
4*.
(a) Find iL and the power supplied by the 4 A source.
(b) Transform the practical current source (8 Ω, 4 A) into a practical voltage
source, and find iL and the power supplied by the new ideal voltage source.
(c) What value of RL will absorb the maximum power, and what is the value
of that power?
iL R L
2Ω
8Ω
6V
5*.
4A
(a) Find the The'venin equivalent of the following two-terminal network:
50 Ω 0.2vab
200 Ω
0.01v ab
100 Ω
a
v ab
b
(b) Find the Norton equivalent of the network shown in the following Figure:
a
50 Ω
100 Ω v1
200 Ω
0.1v1
b
6**.
How many trees may be connected for the following circuit? Draw a suitable tree.
And also determine i3 and power of the dependent source.
-65Ω
8Ω
i3
25 V
7**.
12Ω
9A
10 i3
(a) Determine the The'venin equivalent at terminals a and b for the following
network. How much power would be delivered to a resistor connected to
a and b if Rab equals (b) 50 Ω; (c) 12.5 Ω?
10Ω
50 V
a
100 V
25Ω
15Ω
b
`
8**.
Use source transformation and resistance combination to simplify the
following Figure (a) and (b) until only two elements remain to the left
of terminals a and b.
120 cos 400 t V
60Ω
10Ω
120Ω
6kΩ
a
50Ω
2kΩ
b
( a)
9**.
3kΩ
3.5kΩ
20mA
a
12kΩ
b
(b)
From the following circuit;(a) determine the value of RL which a maximum
power can be delivered, and (b) calculate the voltage across RL (+ reference
at top).
20Ω
10 i1
i1
RL
40Ω
50 V
10***. Determine the The'venin equivalent circuit for terminals: (a) aa';(b) bb' and (c) cc'.
-77Ω
a
a'
10Ω
3Ω
b b'
20Ω
2A
50 V
c c'
11***. Construct a suitable tree for the following circuit and assign tree-branch voltages.
Write KCL and control equations, and find i2.
50Ω
v3
i2
5 i2
45Ω
30Ω
0.02v1
100 V
20Ω
v1
0.2 v3
12***. Construct a tree for the circuit shown in the following Figure in which i1 and i2
are link currents. Write loop equations and solve for i1.
10 A
3Ω
240 V
i1
6Ω
12Ω
30Ω
**********************
i2
60 V
-8CHAPTER 3
INDUCTANCE AND CAPACITANCE
1*.
(a) Waveform of the current in a 3H inductor is shown in Figure, determine the
inductor voltage and sketch it.
i(t) (A)
1
t(s)
−1
0
1
2
3
(b) Find the inductor voltage that results from applying the current waveform
shown in the following Figure.
i(t) (A)
1
−1
t(s)
0
− 0.1
2*.
1
2
3
2.1
(a) Suppose that the voltage across a 2H inductor is known to be 6 cos 5t V.
What information is then available about the inductor current?
(b) Find the maximum energy stored in the inductor of the following Figure.
How much energy is dissipated in the resistor in the time during which the
energy is being stored and recovered in the inductor?
0.1Ω
πt
12sin A
6
3H
-9-
3**.
(a) Determine the maximum energy stored in the capacitor and energy dissipated
in the resistor over the interval 0 ≤ t ≤ 0.5 s .
100 sin 2π tV
20µF
1MΩ
AC
(b) Write nodal equations for the following circuit.
L
vS
4**.
C1
v1
iL
v2
R
C2
iS
(a) Find Leq for the following network.
0.4 µ H
L eq
1µ H
7µ H
5µ H
0.8µ H
12 µ H
5µ H
2µ H
(b) Find Ceq for the following network.
0.4µ F
Ceq
1µ F
7µ F
5µ F
0.8µ F
12 µ F
5µ F
2µ F
******************
- 10 CHAPTER 7
THE SINUSOIDAL FORCING FUNCTION
1.
A sine wave,f(t), is zero and increasing at t =2.1 ms and the succeeding positive
maximum of 8.5 occurs at t =7.5 ms. Express the wave in the from f(t) equals (a) C1
sin(ωt + φ), where φ is positive, as small as possible, and in degrees; (b) C2 cos (ωt + β),
where β has the smallest possible magnitude and is in degrees; (c) C3 cos ωt + C4 sin ωt.
2.
(a) If -10 cos ωt + 4sin ωt = A cos(ωt + φ), where A > 0 and -180° < φ ≤ 180°,
find A and φ. (b) If 200 cos (5t + 130°) = F cos 5t + G sin 5t, find F and G. (c) Find
three values of t, 0 ≤ t ≤ 1 s, at which i(t) = 5 cos 10t - 3 sin 10t = 0. (d) In what time
interval between t = 0 and t = 10 ms is 10 cos 100πt ≥ 12 sin 100πt?
3.
Given the two sinusoidal waveforms, f(t) = -50 cos ωt - 30 sin ωt and g(t) = 55
cos ωt -15 sin ωt , find (a) the amplitude of each, and (b) the phase angle by which f(t)
leads g(t).
4.
Carry out the exercise threatened in the text by substituting the assumed current
response of Eq. (3), i(t) = A cos (ωt - θ), directly in the differential equation, L(di/dt) +
Ri = Vm cos ωt, to show that values for A and θ are obtained which agree with Eq.(4).
5.
Let vs = 20 cos 500t V in the circuit of Fig. 7.8. After simplifying the circuit a
little, find
iL(t).
Figure 7-8
6.
If is = 0,4 cos 500t A in the circuit show in Fig. 7.9, simplify the circuit until it is
in the form of Fig. 7.4 and then find (a) iL(t); (b) ix(t).
Figure 7-9
- 11 7.
A sinuoidal voltage source vs = 100cos 105t V, a 500 ohm resistor, and an 8 mH
inductor are in series. Determine those instants of time, 0 ≤ t < ½ T, at which zero power
is being:(a) delivered to the resistor; (b) delivered to the inductor; (c) generated by the
source.
8.
In the circuit of Fig. 7.10, let vs = 3 cos 105t V and is = 0.1 cos 105t A. After
making use of superposition and Thevenin's theorem, find the instantaneous values of iL
and vL at t = 10 µs.
Figure 7-10
9.
Find iL(t) in the circuit show in Fig. 7.11.
Figure 7-11
10.
Both voltage sources in the circuit of Fig. 7.12 are given by 120 cos 120πt V. (a)
Find an expression for the instantaneous energy stored in the inductor, and (b) use it to
find the average value of the stored energy.
Figure 7-12
- 12 11.
In the circuit of Fig. 7.12, the voltage sources are vs1 = 120 cos 400t V and vs2 =
180 cos 200t V. Find the downward inductor current.
12.
Assume that the op-amp in Fig. 7.13 is ideal (Ri = ∞, R0 = 0, and A = ∞). Note
also that the integrator input has two signals applied to it, -Vm cos ωt and vout. If the
product R1C1 is set equal to the ratio L/R in the circuit of Fig. 7.4, show that vout equals
the voltage across R ( + reference on the left) in Fig. 7.4.
Figure 7-13
13.
A voltage source Vm cos ωt, a resistor R, and a capacitor C are all in series. (a)
Write an integrodifferential equation in terms of the loop current i and then differentiate it
to obtain the differential equation for the circuit, (b) Assume a suitable general form for
the forced response i(t),substitude it in the differential equation, and determine the exact
form of the forced response.
********************************
- 13 CHAPTER 8
THE PHASOR CONCEPT
1*.
(a) Find the complex voltage across the series combination of a 500 Ω resistor
and a 95 mH inductor if the complex current 8 ej3000t mA flows through the
two elements in series.
(b) Transform the time-domain voltage v(t) = 100 cos (400 t - 30º) into the
frequency domain.
2*.
(a) Transform each of the following functions of time into Phasor form:
(i) -5 sin (580t - 110º); (ii) 3 cos 600t-5sin (600t + 110º); (iii) 8 cos (4 t- 30º) +
4 sin (4t - 100 º).
(b) Find the current i(t) in the following circuit:
1.5kΩ
i(t)
40sin 3000tV
AC
3**.
1kΩ
1
H
3
1
µF
6
Determine the admittance (in rectangular form) of (a) an impedance Z = 1000 +
j 400 Ω; (b) a network consisting of the parallel combination of an 800Ω resistor,
a 1 mH inductor, and a 2 nF capacitor, if ω = 1 M rad/s ; (c) a network consisting
of the series combination of an 800Ω resistor, a 1 mH inductor, and a 2 nF
capacitor, if ω = 1 M rad/s .
******************
- 14 CHAPTER 9
THE SINUSOIDAL STEADY-STATE RESPONSE
1*.
Determine the time-domain node voltages v1(t) and v2(t) in the following circuit.
- j5Ω
v1
v2
ο
1∠0 A
- j10Ω
5Ω
2*.
j5Ω
10Ω
0.5∠ − 90ο A
Determine the time-domain currents i1 and i2 in the following circuit.
10cos103 tV
AC
3**.
j10Ω
500µ F
3Ω
i1
4m H i 2
2 i1
Use superposition and find V1 in the following Figure. Also find the The'venin
equivalent faced by the parallel combination of – j5 Ω capacitor and j10 Ω
inductor.
- j5Ω
v1
v2
ο
1∠0 A
5Ω
- j10Ω
j10Ω
j5Ω
10Ω
0.5∠ − 90ο A
4**. Construct plots of the amplitude and phase of Zin versus ω for the following circuit.
0 .1 H
Zin
0.1 F
******************
1
H
40
- 15 CHAPTER 10
AVERAGE POWER AND RMS VALUES
1*.
(a) Time-domain voltage ,v is 4 cos (πt/6) V. Find the power relationships that
result when the corresponding Phasor voltage v = 4 ∠ 0º V is applied across
an impedance Z = 2 ∠60° Ω.
(b) Find the average power being delivered to an impedance ZL = 8- j11Ω by a
current I = 5 ∠20°A.
2*.
(a) Find the average power absorbed by each of the three passive elements and
the average power supplied by each source.
- j2Ω
j2Ω
20∠0ο V
10∠0ο V
2Ω
(b) Find the average powers delivered to a 4Ω resistor by the current i1 = 2 cos
10 t – 3 cos 20 t A and i2 = 2 cos 10t – 3 cos 10 t A.
3**.
(a) Calculate the average power delivered to each of the two loads, the apparent
power supplied by the source, and the power factor of the combined loads.
60∠0ο Vrms
2 − j1Ω
1 + j5Ω
(b) An industrial consumer is operating a 50 kW (67.1 hp) induction motor at 0.8
PF, lagging. The source voltage is 230 V rms. In order to obtain lower
electrical rates, the consumer wish to raise the PF to 0.95 lagging. Specify an
arrangement by which may be done.
******************
- 16 CHAPTER 11
POLYPHASE CIRCUITS
1*.
A balanced 3-phase system has a line voltage = 300 V rms and supplying a
balanced Y-connected load with 1200 W at a leading PF of 0.8. What are the
line current and the per-phase load impedance? If 600 W lighting load is
added (in parallel) to the system, determine the line current and power generated
by the source.
2*.
Determine the amplitude of the line current in a 300 V rms, 3-phase system which
supplies 1200 W to a ∆ connected load at a lagging PF of 0.8. When load is
changed to Y connection, find the phase impedance.
3**.
Determine the power delivered to each of the three loads and the power lost in the
neutral wire and each of the two lines.
1Ω
ο
115∠0 Vrms
50Ω
20Ω
100Ω
j10Ω
3Ω
115∠0ο Vrms
1Ω
4***. In the following Figure, add 1.5Ω resistance to each of the two outer lines, and
2.5Ω resistance to the neutral wire. Find the average power delivered to each of
the three loads.
1Ω
115∠0ο Vrms
50Ω
20Ω
100Ω
j10Ω
3Ω
115∠0ο Vrms
1Ω
******************
- 17 CHAPTER 14
MAGNETICALLY COUPLED CIRCUITS
1*.
Determine the output voltage across the 400 Ω resistor to the source voltage.
M =9H
1Ω
V1 = 10∠0ο V
1H
ω =10 rad/s
2*.
100 H
400Ω
v2
Write the correct set of equations for the following circuit.
5Ω
V1
1F
7H
6H
3Ω
M =2H
3**.
Find the T equivalent and Π equivalent of the linear shown in the following:
40mH
30 m H
6 0 mH
******************
- 18 CHAPTER 15
GENERAL TWO-PART NETWORKS
1*.
Calculate the input impedance of the following network. And use admittance
matrix to again find the input impedance.
20Ω
5Ω
10Ω
v1
2*.
1Ω
2Ω
4Ω
(a) Find the input impedance.
0.5I a
5Ω
1Ω
10Ω
v1
2Ω
Ia
4Ω
(b) Find the four short-circuit admittance parameters for the resistive two-port.
10Ω
v1
3**.
I1
5Ω
I2
20Ω
v2
In an approximate linear equivalent of a transistor amplifier, the emitter is the
bottom node, the base is the upper input node and the collector is the upper output
node. 2000 Ω resistor is connected between the collector and base. Determine the
performance of the amplifier.
4***. Find [z] for the two-port shown in the following:
- 19 50Ω
20Ω
v1
25Ω
50Ω
20Ω
v2
40Ω
v1
( a)
25Ω
(b)
5***. Find [h] for the two-port shown in the following:
20Ω
v1
10Ω
40Ω
v2
v1
40Ω
( a)
v2
(b)
6***. Find [h] for the two-port shown in the following:
6Ω
v1
12Ω
10Ω
12Ω
v2
( a)
v1
2I 2
10Ω
I2
(b)
**************************
Note :
*
**
***
Must Know Questions
Should Know Questions
Could Know Questions
v2
v2
- 20 -