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1

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


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


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


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


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


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


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?

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


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



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



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



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



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.

rabinr

Line

rabinr

Typewritten Text

KB-3

rabinr

Typewritten Text

PA-2

rabinr

Typewritten Text

PA-3

rabinr

Line

rabinr

Line

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