MA230
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Transcript of MA230
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8/9/2019 MA230
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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
Page 2 of 4
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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]
Page 3 of 4
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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
Page 4 of 4