PAPER CODE ........ELEC209............ PAGE .. ..... 1.............. OF ....9..........................CONTINUED.
FIRST SEMESTER EXAMINATIONS 2020/21

ELECTRICAL CIRCUITS & POWER SYSTEMS

TIME ALLOWED: Three Hours- + One Hour

INSTRUCTIONS TO CANDIDATES
This is a time-controlled unseen exam.

The numbers in the right hand margin represent an approximate guide to the marks available for that
question (or part of a question). Total marks available are 100.

Copying any material from another source, or colluding with any other person in the
preparation and production of this work will be considered suspected academic misconduct and
will be dealt with according to the University’s Academic Integrity Policy.

Instructions:
You must provide your solutions as detailed as possible. Failure to do this results in loosing marks.
Marks are allocated for the steps as well as the final answers, so you must show all the intermediate
steps.

PAPER CODE NO. EXAMINER: Dr. A. Al-Ataby
ELEC209 DEPARTMENT: EE&E Email: aliataby@liverpool.ac.uk

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1 a) For the three-phase system shown in Figure Q1-1, determine the reading of
each Wattmeter W1 and W2, then determine the total power delivered to the
Y-load. Assume Van = 120 V.

Figure Q1-1

5
b) For the three-phase system shown in Figure Q1-2, assuming EAN = 120 V and
ZY = 6 + j8 Ω,

Figure Q1 - 2

i) Find the line currents 6
ii) Find the phase voltages at the load 4
iii) Find the line voltages at the load. 3
iv) Find the total real power and reactive power delivered to the load.

2
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c) Figure Q1-3 shows a circuit with three coils in series. Coils L1 and L2 interact,
while L3 doesn’t interact with other coils. Find the total inductance of the
circuit LT.

Figure Q1-3

5

Total
25
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2. a) For the circuit shown in Figure Q2-1,

Figure Q2 -1
Find the voltages v1 and v2, and the currents i1, i2, i3, i4 and i5 immediately
after closing the switch.

5
b) For the circuit shown in Figure Q2-2 below:

Figure Q2-2

The switch was in position 1 for a long time. It is then thrown to position 2
for 2 s, then returned back to position 1.

i) Find the mathematical expression(s) for the voltage v for t ≥ 0.

6
ii) Find the mathematical expression(s) for the capacitor current for t ≥ 0. 4

c) It is required to design an RC timer circuit, with a switch, a capacitor C
(1 µF) and a resistor R, all in series with a 50 V power supply. Closing the
switch then opening it after 5 s produces 3 V across the capacitor. Design this
circuit (i.e. find the value of R) to satisfy this condition.

6
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d) A 0.1 µF capacitor is initially charged to 230 V, then discharged through a
3 MΩ resistor. Find the capacitor voltage after 0.2 s from the start of
discharging.

4

Total
25

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3. a) A power system is shown in Figure Q3 below. A 50 MW load with 0.8
power factor lagging connected to the 33 kV substation transformer is
required to maintain 30 kV. [Note that the system is a three-phase one.]

Figure Q3

i) Calculate the terminal voltage VG of the generator G in pu.

8
ii) Redraw a simpler diagram for the system in per unit standard (i.e.
all the equipment/components, voltages and currents should be in
pu).

5
b) An electrical heater is rated at 100 V, 500 W. Compute the actual and
per unit impedance of the heater. Draw the per unit equivalent circuit of
the heater.

4
c) Find the voltage across the open-circuited secondary of a magnetically
coupled circuit when 35 V at 400 Hz is applied to the primary circuit.
(self-inductances of coil 1 and 2 are 0.75 H and 0.83 H, respectively, and
the coupling coefficient is 0.6).

5
d) What is the maximum value of the mutual inductance that a
magnetically-coupled circuit could have between the two coils involved
if each has a self-inductance of 0.4 H and 0.8 H, respectively?
3

Total
25
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4. a) A fossil fuel power plant generating 670 MW is planned to be replaced by a
wind farm. Determine the number of wind turbines needed to replace the
power plant, assuming average wind speed is 13 m/s, wind turbine efficiency
is 39% and blade length is 56 m. [Note: as the number of turbines needs to be
density of air is 1.25 kg/m3).

5
b) A three-phase, 22 kV (phase), 500 MVA (phase) star-connected synchronous
generator has a per phase reactance Xs of 1.5 pu and supplies 0.8 pu per phase
real power at the rated voltage, with a lagging power factor of 0.6 to the load.

i) Calculate the actual excitation voltage and the power angle.

4
ii) Calculate the actual complex power consumed by the load in MVA (per
phase).
4
c)

A three-phase induction machine, with rated frequency of 60 Hz and rated
voltage of 220 V, has the following parameters: R1 = 0.39 Ω, R2' = 0.14 Ω,
x1 = 0.35 Ω and x2' = 0.35 Ω. Calculate input power of the machine, stator
current, slip and power factor under rated condition (assume the rated speed is
1746 rpm).

8
d)

Two transformers (4:1 and 1:3) are connected together (cascaded). The two
transformers are powered by a 10 V AC supply (with a source resistance value
of 6 Ω) connected to the primary winding of the first transformer, and a load
with 9 Ω is connected across the secondary winding of the second transformer.
Find the current in the primary loop of the first transformer and the power