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Course Number Section Basic Circuit Analysis ELEC 273 R Examination Date Time # of pages
Final December 7th, 2011 3 hours 4 Instructor(s) Dr. G. Cowan
Materials allowed: No Yes (Please specify) Calculators allowed: No Yes
X
X
Students are allowed to use one of the Faculty of Engineering and Computer Science’s two approved
calculators. Calculators must be identified with an ENCS sticker. Special Instructions:
Attempt all questions.
Show all steps clearly in neat and legible handwriting.
Students are required to return question paper together with exam booklet(s).
Maximum total score is 60 marks
Question
Value
Grade earned
1
10
2
10
3
10
4
10
5
10
6
10
Total
60
2
Question 1 (10 marks): Consider the circuit in Figure 1.
(a) Using MESH ANALYSIS, determine the unknown mesh currents i1, i2, i3, and i4.
(b) Find the power absorbed by the -5 V voltage source.
1 A
1 W
2 W
4 W
3 W
3 V
2 W
8 W
10 W
-5 V
3 A
6 W4 V
i1 i2 i3
i42 W
Figure 1: Circuit for Question 1
Question 2 (10 marks): Use SUPERPOSITION and NODAL ANALYSIS to solve the circuit in Figure 2 for the
labeled node voltages, v1 and v2. Give your answer in the time domain. (10 marks)
2 H3cos(12t) V
5 V
8 W
10 W
30 W 1 H
5 mF
8 mF v1 v2
Figure 2: Circuit for Question 2.
3
Question 3 (10 marks):
2 Ωt = 0 s
0.1 F8 Ω
24 Ω6 Ω
6 Ω64 V-1 A0.5 A +
vC
-
Figure 3 : Circuit for Question 3
In the circuit in Figure 3, the switch has been in the left position for a long time. It switches into the right-hand
position at t = 0 s.
3a) Find the value of vC for t = 0- and as t → ∞. (2 marks)
3b) Find expressions for vC(t) and ic(t) for t > 0. (6 marks)
3c) Sketch vC(t) and iC(t) for -1 s < t < 5 s. Please be sure to label your axes. Indicate the value of vC(t) and
iC(t) for t = 0.5 s. (2 marks)
Question 4 (10 marks). In Figure 4 a voltage source is applied a load consisting of four elements. The voltage
source, vs(t) = 10 cos(100 t) V.
1 mF
1 mF
10cos(100t) V
8 W
50 mH
+ VR -+
VC
-
+
VLC
-
IS
Figure 4: Circuit for Question 4.
a) Determine the phasor representation of the source voltage, the current it supplies and each of the labeled voltages.
That is, find: VS, IS, VR, VC, and VLC.
b) Find each of the quantities in a) as a function of time. That is, find iS(t), vR(t), vC(t), and vLC(t).
c) Draw the following phasors in the complex plane: VS, IS, VR, VC, and VLC.
d) Find the average power dissipated in this 4 element load.
4
Question 5a (7 marks). Consider the operational amplifier circuits shown in Figure 5. You may assume that the
operational amplifiers are ideal.
i. Find the gain of the circuit on the left: AV1 = vo1/vs1.
ii. Find the gain of the circuit on the right: AV2 = vo2/vs2.
RS
vo1
vs1
R1
R2
is1
vs2
vo2
R1
R2
RSis2
Figure 5: Circuit for Question 5a
Question 5b: (3 marks) For the cascade of operational amplifiers shown below in Figure 6, find the overall gain:
AV = vo2/vs1.
RS vo1
vs1
R1
R2
is1
vs2
vo2
R1
R2
Figure 6: Circuit for Question 5b
Question 6 (10 marks). For the circuit in Figure 7, the capacitor is connected to the current source for t < 0 s. At
t = 0 s the switch changes position and connects the capacitor to the 6.4 W resistor. The switch remains in this
position for t > 0 s.
6.4
Ω
IS=2 mA
VS=10 V
+ vC -
0.0625 F iL
0.5 H
10
00
Ω
t = 0 s
Figure 7: Circuit for Question 6.
Find vC(t) for 0 < t < .
1
Course Number Section Basic Circuit Analysis ELEC 273 W Examination Date Time # of pages
Final April 12th, 2012 3 hours 4 Instructor(s) Dr. G. Cowan
Materials allowed: No Yes (Please specify) Calculators allowed: No Yes
X
X
Students are allowed to use one of the Faculty of Engineering and Computer Science’s two approved
calculators. Calculators must be identified with an ENCS sticker. Special Instructions:
Attempt all questions.
Show all steps clearly in neat and legible handwriting.
Students are required to return question paper together with exam booklet(s).
Maximum total score is 55 marks
Question
Value
Grade earned
1
10
2
6
3
6
4
8
5
10
6 5
7
10
Total
55
2
Question 1 (10 marks): Consider the circuit in Figure 1. iS = 2sin(100t) A. vS = 14.14cos(100t+45) V
a) Using MESH ANALYSIS in the phasor domain, write and simplify the equations required to determine
the unknown mesh currents I1, I2, and I3. You do not need to solve these equations. You can, however,
check that the following values satisfy your equations:
17286.0
10788.1
16059.0
~
~
~
3
2
1
I
I
I
b) Express i1, i2, and i3 in the time domain.
c) Determine va-b. Express your results both in the phasor domain and the time domain.
9 W
30 mH
0.5 mF 1 mF8 W
12 W
50 mH
10 mH
3 W
20 mH
i1 i2
i3
iS
vS
a
b Figure 1: Circuit for Question 1
Question 2 (6 marks): Consider the circuit in Figure 1 and use results obtained in Question 1.
a) Determine the load impedance that when connected between terminals a-b dissipates the maximum real
average power.
b) Determine the value of this real average power.
Question 3 (6 marks): Consider the circuit in Figure 2. It is identical to that in Figure 1, except for the addition of
the dc current source.
Determine the voltage va-b due to all sources in the circuit in Figure 2. 9 W
30 mH
0.5 mF 1 mF8 W
12 W
50 mH
10 mH
3 W
20 mH
i1 i2
i3
iS
vS
a
b
iDC = 2 A
Figure 2: Circuit for Question 3.
3
Question 4 (8 marks):
t = 0 s3 H
2 Ω
24 Ω
8 Ω64 V
2 Ω
iL
Figure 3 : Circuit for Question 4
In the circuit in Figure 3, the switch has been open for a long time. It closes at t = 0 s.
4a) Find the value of iL for t = 0- and as t → ∞. (2 marks)
4b) Find expressions for iL(t) and vL(t) for t > 0. (4 marks)
4c) Sketch vL(t) and iL(t) for -1 s < t < 3 s. Please be sure to label your axes. Indicate the value of vL(t) and
iL(t) for t = 1 s. (2 marks)
Question 5 (10 marks). In Figure 4 a voltage source is applied across several loads. The voltage source,
vs(t) = 5 cos(1000t) V.
5 W vS
0.2 mF5 mH
0.1 mF
20 mH
0.2 mF10 mH
iC iR iL iLC1 iLC2 iT
Figure 4: Circuit for Question 5.
a) Determine the phasor representation of vs, iC, iR, iL, iLC1, iLC2 and iT. That is, find: VS, IR, IC, IL, ILC1, ILC2 and IT.
b) Find each of the quantities in a) as a function of time. That is, find iT(t), iR(t), iC(t), iL(t), iLC1(t), iLC2(t).
c) Draw the following phasors in the complex plane: VS, IT, ILC1, ILC2, and IR.
d) Find the complex power ( S~
) supplied by the source to the elements inside the dashed box. Indicate how much
real power is delivered to this load and how much reactive power is delivered. Give appropriate units for all
answers.
4
Question 6 (5 marks). Consider the operational amplifier circuit shown in Figure 5. You may assume that the
operational amplifiers are ideal.
i. Find the gain of the circuit: AV = vo1/vs1.
RS
vo1
vs1
R3
R4
R1
R2
RL
Figure 5: Circuit for Question 6
Question 7 (10 marks). For the circuit in Figure 6, the capacitor is connected to the 5 W resistor for t < 0 s. At t = 0 s
the switch changes position and connects the capacitor to the current source. The switch remains in this position
for t > 0 s. 5
Ω
IS=3 A
VS=10 V
+
vC
-0.25 F
iL
1 H
1.1
54
7 Ω
t = 0 s
Figure 6: Circuit for Question 6.
a) By righting and solving the appropriate differential equation, find iL(t) for 0 < t < .
b) Is iL(t) showing an over damped, critically damped, or under damped response? Explain. Though you have
not solved for vC(t), what type of damping will its solution exhibit?
Page 1 of 6
Course Number Section Basic Circuit Analysis ELEC 273 R Examination Date Time # of pages
Final December 17th, 2014 2 pm 4 Instructor(s) Dr. Cowan, Glenn
Materials allowed: No Yes (Please specify) Calculators allowed: No Yes
X
X
ENCS approved calculators are allowed. Special Instructions: All questions must be answered in the examination booklet. If required, use the back of the given pages for
showing the work. For Section II show all important steps leading to final answers. Maximum mark is 60.
Name (underline family name) :
Concordia Student ID :
Question Marks
Section I 30
Section II
1 10
2 10
3 10
Total: 60
Basic Circuit Analysis Wednesday, December 17th, 2014
ELEC 273, Section R Final
Page 2 of 6
Section I) Multiple Choice Questions: There are _____ multiple choice questions. Please circuit the most appropriate answer for each one on the question paper. 1) The waveform below is the voltage across a capacitor of value C = 3 μF. The current at t = 3 ms is:
t (ms)
v(t) (V)
5
1 2 3 4
2) For the capacitor waveform above, the energy stored at t = 1.5 ms is: a) 5.75 μJ b) 11.25 μJ c) 37.5 μJ d) 56.25 μJ e) 75 μJ f) 84.375 μJ
3) The waveform below is the voltage across an inductor of value L = 4 mH. Assume v(t) = 0
for t < 0. The current at t = 3 s is:
t (s)
v(t) (V)
2
1 2 3 4
4) Below is the phasor diagram for a load under sinusoidal steady-state operation. |V1| = 15 V, |I1| = 10 A. The average power absorbed is:
Re
Im
I1V1
60 deg.50 deg.
a) -7.5 mA b) 3.75 mA c) -2.5 mA d) 33.75 mA
a) 0 A b) 0.5 mA c) 1 mA d) -8 mA e) Insufficient information to determine
a) 25.65 W b) 51.30 W c) 73.86 W d) 75 W e) 150 W
Basic Circuit Analysis Wednesday, December 17th, 2014
ELEC 273, Section R Final
Page 3 of 6
5) For the circuit below, the value of the load resistor that dissipates the maximum power is:
RL4 W
12 W
6) The circuit below has reached dc steady state. The voltage across the capacitor (VC) is:
6 W
3 V3 W
3 W
0.1 F
1 H
+ VC -
+
VL
-
7) The circuit above in Question 6 has reached dc steady state.The voltage across the inductor (VL) is:
8) The combination of R and L will have a complex impedance at ω = 10 rad/s. A designer wants to put another element in parallel with it to make the overall impedance between terminals a-b be real. What is the element and its value to be put in parallel:
10 W
1.732 H
E
L
E
M
E
N
T
a
b
a) L = 2.3 H b) L = 4.3 mH c) C = 4.3 mF d) C = 5.61 mF e) C = 17.83 mF
a) 0 V b) 1 V c) 2 V d) 2.4 V e) 3 V
a) 0 Ω b) 3 Ω c) 4 Ω d) 8 Ω e) 12 Ω f) 16 Ω
a) 0 V b) 1 V c) 2 V d) 2.4 V e) 3 V
Basic Circuit Analysis Wednesday, December 17th, 2014
ELEC 273, Section R Final
Page 4 of 6
9) Consider the 2nd order circuit below.
+ vC -
L
CR
vs=u(t)
Which of the following 2nd order responses would occur for vc if the circuit were under-damped circuit?
(a) (b) (c) 10) What element value can be changed in the second order circuit in question 9 in order to make the circuit become overdamped:
11) In the circuit below, R1 = 4 Ω, R2 = 6 Ω, R3 = 8 Ω,which resistor dissipates the least power?
VSR3
R2R1
a
b
12) Find the current I in the circuit below:
a) Increase C b) Increase L c) Increase R d) Decrease R d) Increase R or increase C or increase L e) Increase R or increase C or decrease L
a) R1 b) R2 c) R3 d) Either R1 or R3
Basic Circuit Analysis Wednesday, December 17th, 2014
ELEC 273, Section R Final
Page 5 of 6
2vx
-
vx
+
1 W 1 A
1 W
I=?
13) Find vo in the circuit below, assuming the opamp is ideal.
R3 = 1 kW
R1 = 1 kW
vo
2 V
R2 = 1 kW
3 mA
a) 5/4 A b) 3/4 A c) 1/4 A d) -7/4 A
a) -3.0 V b) -1.5 V c) -1.0 V d) 1.0 V e) 1.5 V f) 3.0 V
Basic Circuit Analysis Wednesday, December 17th, 2014
ELEC 273, Section R Final
Page 6 of 6
Part II: Long Answer 1) Determine and draw the Thevenin Equivalent Circuit for the circuit below, considering terminals a-b. Use IS = 1 A, VS = 4 V.
a
b
IS
VS
1 W
2 W
2 W
2 W
2) Find the total current through the inductor L, iL(t). v1(t) = 0.1 cos(1000t), V2 = 3 V, I1 = 1 A,
R2 = 2 Ω, R1 = 1 Ω, C1 = 500 μF, C2 = 40 μF, L = 1 mH. Sketch v(t).
5vx
+
vx
-
v1(t) V2
C1 C2
R1
R2 L
I1
v(t)
iL(t)
3) The circuit below has reached dc steady-state before the swith opens at t = 0. C = 1 F, L =
10 mH, R1 = 100 W Choose R such that the circuit below is critically damped for t > 0. Then write the differential equation governing the circuit for t > 0 and solve for iL(t). Vs = 4 V. is = 0.2u(-t) A. (is is the time reversed unit step. 2 A for t < 0. 0 for t > 0.)
is
iL
+
vC
-
R1
t = 0 s
VSLC
R
Without resolving the circuit, draw the Thevenin equivalent circuit if IS = -2A and VS = -8V.
Based on the solution to iL(t), find an expression for the energy stored
in the capacitor as a function of time for t > 0.
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