Final Exam Circuit

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INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA

END OF SEMESTER EXAMINATION

SEMESTER I, 2005/2006 SESSION

KULLIYY H OF ENGINEERING

Programme : ENGINEERING Level of Study : UG 1

Time : 9:00 am - 12:00 Noon Date : 26/10/2005

Duration : 3 Hrs

Course Code : ECE 1311 Section(s) : 1

Course Title : Electric Circuits

This Question Paper Consists of Seven (7) Printed Pages (Including Cover Page)

With Six (6) Questions.

INSTRUCTION(S) TO CANDIDATES

DO NOT OPEN UNTIL YOU ARE ASKED TO DO SO

•

Total marks of this examination is 100.• This examination is worth 40% of the total assessment.

• Answer any 5 (Five) questions.

Any form of cheating or attempt to cheat is a serious

offence which may lead to dismissal.



2

[Answer any 5 (FIVE) questions.]

Q.1 [20 marks]

(a) The current entering the positive terminal of a device is t et i

23)(−

= A. Find the

charge delivered the device between 0=t and 2=t s. (3 marks)

(b) The charge flowing in a wire is plotted in Fig. 1. Sketch the corresponding

current. (6 marks)

(c) For the circuit in the circuit of Fig. 2, find 1i and 2i . (2+2 marks)

Fig. 2

(d) Find the equivalent resistance R ab in the circuit in Fig. 3. (7 marks)

20 mA 6 k Ω 4 k Ω

i1 i2

Fig. 1

13Ω

9Ω

30Ω

20Ω

15Ω

50Ω

7Ω

a

bFig. 3

0 1 2 3 40

5

10

q ( C )

t (s)



3

Q.2 [20 marks]

(a) Use the nodal analysis to write three independent equations in terms of the

node voltages 1v , 2v and 3v of the circuit shown in Fig. 4. (6 marks)

Find the node voltages 1v , 2v and 3v and calculate I. (4 marks)

Fig. 4

(b) Based on Fig. 5 below;

Fig. 5

(i) Use the mesh analysis method to write three independent equations in terms

of the currents i1, i2 and i3 for the circuit shown in Fig. 5 by direct

inspection. (6 marks)

(ii) Find currents i1, i2 and i3. (4 marks)

5 A 4 Ω 2 Ω 8 Ω

12 V

8 Ω 4 Ω

2 Ω

2 A

1v 2v3v

I

Ω Ω

Ω

Ω

Ω

i1 i2 i3

1k1k

12V1k

10V

20V

1k

1k



4

Q.3 [20 marks]

(a) Based on the circuit in Fig. 6 below;

Fig. 6

(i) Use superposition to obtain v x in the circuit. (8 marks) (ii) Use source transformation to obtain v x in the circuit. (4 marks)

(b) Based on the circuit in Fig. 7 below;

Fig. 7

(i) Find the Thevenin equivalent circuit across the terminals a-b. (6 marks) (ii) Find the maximum power transfer P max that can be delivered to the resistor

R in the circuit. (2 marks)

10 Ω 25 Ω

20 Ω5 Ω

60Va b

30 Ω 10 Ω

+ v x -

60 Ω 6 A 30 Ω

20 Ω

40 V90 V



5

Q.4 [20 marks]

(a) Find the equivalent capacitance and inductance with respect to the terminals a-b

for the circuits shown in Fig. 8. (3+3 marks)

Fig. 8

(b) The switch in Fig. 9 has been in position a for long time. At t = 0, it moves to

position b. Calculate v(t) for t>0. (6 marks)

Fig. 9

(c) Based on the circuit diagram of Fig. 10, find )(t io

(i) if the switch has been opened for a long time and is closed at t =0, and

(ii) if the switch has been closed for a long time and is opened at t =0.

(4+4 marks)

Fig. 10

30 V 12 V

a

b

6 Ω

3Ω 2 F

t =0

12 V

2 Ω

4 Ω 8 H io

t =0

-

a

b

10 µF 30 µF

20 µF 5 µF 80 µF

15 mH

6 mH

8 mH6 mH

8 mH

4 mH

b

8 mH

5 mH

6 mH



6

Q.5 [20 marks]

(a) Use the mesh analysis method to write two independent equations in terms of

the currents I1 and I2 of the circuit shown in Fig. 11. Do not use any other

variables in your equations. Solve for currents I1 and I2. (6 marks)

Fig. 11

(b) Find io in the circuit of Fig. 12 using superposition principle. (6 marks)

Fig. 12

(c) For the circuit shown in Fig. 13, find the Thevenin equivalent circuit at

terminals a-b. (8 marks)

Fig. 13

1 Ω 1 Ω

1 Ω

1 H 1 H

1 F

t v 4cos101 ⋅= )304cos(202

ot v −⋅=

i1 i2

4 Ω 2 Ω

8 V1 H

t v 4cos200 ⋅=

io

• a b •

10 C

13 Ω

10 Ω

8 Ω

20 H

12 Ω

60 cos (4t + 45o)V



7

Q.6 [20 marks]

(a) Calculate i(t) in the circuit of Fig. 14. (8 marks)

Fig. 14

(b) Find rms value of the waveform shown in Fig. 15. (4 marks)

Fig. 15

(c) Obtain power factor for each of circuits in Fig. 16. Specify each power factor as

either leading or lagging. (4+4 marks)

Fig. 16

1 2 3 4

5

0

-5

t

v(t)

5 Ω

10 mH

5 mF

3 Ω

i(t)

v=6.cos(200t+30o)

4 Ω

-j2 Ω -j2 Ω

5 Ω

2 Ω 1 Ω

-j1 Ω 4 Ω

1 Ω

(i) ii

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Final Exam Circuit