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Sri Lanka Institute of Information Technology

B.Sc. Eng. Honours Degree inEngineering

Final ExaminationYear 1, Semester 1 (2014)

EC102 - Electrical Systems

Duration: 2 Hours

May 2014

Instructions to Candidates:

•  This paper contains 4 questions on 4 pages (including the cover page).

•   Answer  all questions

•   All questions do not carry equal marks. The marks assigned for each part of aquestion is indicated in brackets.

•  This examination accounts for 70% of the module assessment.

•  You are permitted to use  CALCULATORS

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Question 1: (25 marks)

DC Analysis of Circuits :– A resistive network with two voltage sources and one

current source is shown in Figure Q1a. The part of the circuit left of the points AB

is highlighted with a dashed box. The current through  R2  is I. Answer the following

questions.

R1   6kΩ2mAI

R2

10kΩ

R3   5kΩ

E 1   10V

R4

12kΩ

R5   4kΩ

8VE 2

A

B

I

Figure Q1a

(a) Use the source transformation method to replace the current source and the

resistor inside the highlighted box with a voltage source and a resistor.[5 marks]

Note :– Pay special attention to the direction of the source when calculating.

(b) Use the superposition theorem together with nodal analysis on the circuit mod-

ified in part (a) to find the current   I  through resistor  R2. Do not reduce the

circuit any further. [20 marks]

Note :– your solution should include (i) clearly marked sub-circuits, (ii) the di-rection of voltage across its components marked with arrows.

Question 2: (15 marks)

Magnetism :–A series-parallel magnetic circuit made out of sheet steel throughout is

shown in Figure Q2a. The cross section of the of the core is 5 × 10−4m2 in the entire

core. The air gap length is 0.002 m. The core lengths are as follows.   lab   =   lbg   =

lgh  =   lha  = 0.2 m,   lbc  =   lfg  = 0.1 m,   lcd  =   lef   = 0.099 m. Find the value of current

I   required to establish a flux in the gap of Φg   = 2 × 10−4Wb.   µ0   = 4π  × 10

−7,

µr(sheet steel) = 4000.

I 

Air gapN=200 turns

a   b   c

d

e

f gh

Figure Q2a

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Question 3: (35 marks)

Polyphase Circuits :– The Figure Q3a shows a star connected three phase generator

connected to a star connected load. The generator and load are connected together

by transmission lines of zero impedance. The symbols have their usual meaning. The

following voltages are given.   E AN   = 120V  ∠

00

,  E BN    = 120V  ∠−

1200

, and  E CN    =120V  ∠1200.

E AN 

E CN    E BN 

12Ω

− j9Ω

− j9Ω

12Ω

− j9Ω

12Ω

A

C B

a

c   b

N   n

+

–

–

+

–

+

Generator Load

Figure Q3a

(a) Determine the phase voltages at the load. [5 marks]

(b) Determine the phase currents at the load. [5 marks]

(c) Determine the line currents at the load. [5 marks]

(d) Compute the active power dissipated by each phase at the load and the total

active power. [5 marks]

(e) Compute the total reactive power at the load. [5 marks]

(f) Compute the power factor at the load and indicate whether it is leading or

lagging. [5 marks]

(g) Sketch the phasor diagram at the load. [5 marks]

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Question 4: (25 marks)

AC Analysis of Circuits :– A network with one current source and one voltage source

is connected across AB to a load  Z .

50V∠450

+

–

X C 

400Ω

R

400Ω

400ΩX L   100mA∠00

A

B

Z 

Figure Q4a

(a) Find the Thévenin equivalent circuit across AB considering the impedance  Z  as

the load by following the steps given below.

i. Find the Thévenin impedance  Z th  across AB. [10 marks]

ii. Use Nodal analysis to find the open circuit voltage  V  th. [10 marks]

(b) What should be the value of  Z   for maximum power transfer? [5 marks]

End of the Question Paper

Formula Sheet

Finding the determinant of a 2 × 2 matrix

a11   a12a21   a22

=  a11a22 − a21a12.

Finding the determinant of a 3 × 3 matrix

a11   a12   a13a21   a22   a23a31   a32   a33

= a11

a22   a23a32   a33

− a12

a21   a23a31   a33

+ a13

a21   a22a31   a32

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