Sample Question Paper for 9210-137
Graduate Diploma in Mechanical Engineering
Electro techniques
Duration: three hours
You should have the
following for this examination
• one answer book
• non-programmable calculator
• pen, pencil, drawing
instruments
General instructions
• This paper consists of nine questions.
• Answer any five questions.
• A non-programmable electronic calculator may be used but candidates must show
sufficient steps to justify their answers.
• Drawings should be clear, in good proportion and in pencil. Do not use red ink.
• All questions carry equal marks. The maximum marks for each section within a
question are shown.
1
An ac circuit is shown in Figure Q1, where resistances, inductances and capacitance
are indicated. Voltage sources connected to the circuit are given as e1(t) =120sin(314t)
V,e2(t)=80sin(314t+30°) V, and e3(t)=100sin(314t-120°) V.
Figure Q1
2
a)
b)
c)
d)
e)
Calculate inductive and capacitive reactance of capacitors and inductors.
Express time domain quantities e1(t) e2(t) and e3(t) in phasor domain.
Calculate currents I1, I2 and I3 using mesh method.
Determine the voltage at point P.
Calculate complex power developed by the sources.
(3 marks)
(2 marks)
(8 marks)
(4 marks)
(3 marks)
a)
b)
c)
List three applications of transformers.
Explain briefly the losses in transformers.
With the help of suitable sketches, show the following two winding types
of transformers.
i)
Concentric windings.
ii) Sandwiched windings.
Prove that the emf induced in windings of a transformer is given by Erms = 4.44Nf Φm,
where N-number of turns, f-frequency, Φm - peak value of net magnetic flux through
the core.
A 400 kVA, 11000 V/400 V three-phase transformer has per-phase primary and
secondary resistance of 0.48 Ω and 0.0023 Ω respectively. When the transformer
is at no-load it consumes 3.8 kW from the supply.
i)
Calculate the power loss and efficiency when the transformer is connected
to rated load at 0.88 power factor lagging.
ii) What is the new power loss when the load is reduced to 50% of the rated load?
(3 marks)
(4 marks)
d)
e)
3
a)
b)
c)
d)
Explain the types of induction motors based on rotor construction.
List the methods of speed control of induction motors.
Sketch the per-phase equivalent circuit of a three-phase induction motor and
identify its parameters.
A 400 V, 20 kW, 50 Hz, eight pole, three-phase, star connected induction motor
has stator and rotor resistance of 0.35 Ω and 0.15 Ω and leakage reactance of
0.6 Ω and 0.225 Ω respectively. Magnetizing reactance is 15 Ω. Friction and
windage losses are 260 W. The rotor parameters are referred to the stator side.
Calculate the following when the motor is operating at 1.5% slip.
i)
Per-phase equivalent impedance of the motor.
ii) Input power and air gap power.
iii) Stator and rotor copper loss.
iv) Output torque.
2
(1 mark)
(1 mark)
(4 marks)
(5 marks)
(2 marks)
(2 marks)
(3 marks)
(3 marks)
(3 marks)
(4 marks)
(2 marks)
(3 marks)
4
a)
b)
c)
5
a)
b)
Explain with necessary sketches how a megger is used to measure insulation
resistance between conductor and sheath of a two core cable.
i)
Show how two wattmeters can be used to measure power of a three-phase
balanced system.
ii) Derive a formula to determine power factor of the load using readings of the
two wattmeters.
A star connected three-phase balanced load is fed by a 400 V (line-line) three
phase three wire system. The power absorbed by the load is measured using
two wattmeters. The reading of the wattmeters are –1800 W and 3600 W.
Calculate the following.
i)
Three phase power.
ii) Power factor.
iii) Per-phase impedance.
Write down the three NPN BJT configurations, and draw a circuit diagram for each
of them.
Consider the circuit shown in Figure Q5a and convert it into the circuit shown in
Figure Q5b by using Thevenin’s theorem. Calculate the following assuming
VCC = 20 V, VBE = 0.3 V, R1 = 100 K, R2 = 25 K, RC = 4 K, RE = 6 K, β = 50.
i)
Rth
ii) Vth
iii) IB
iv) IC
v) IE
vi) VCE
Figure Q5a
(4 marks)
(4 marks)
(4 marks)
(2 marks)
(3 marks)
(3 marks)
(6 marks)
(2 marks)
(2 marks)
(2 marks)
(2 marks)
(3 marks)
(3 marks)
Figure Q5b
3
See next page
6
a)
b)
c)
Write down four characteristics of an ideal Op-amp.
Explain the following terms of an Op-amp.
i)
Input offset current.
ii) Output offset voltage
Consider the following circuit shown in Figure Q6 and derive the expression for
the output voltage (V0) as
(4 marks)
(2 marks)
(2 marks)
(12 marks)
VO = –CR d(vin)
dt
Figure Q6
7
a)
b)
c)
d)
8
a)
b)
c)
d)
e)
Simplify the following Boolean expressions using Boolean algebra and K – map.
––
– –
i)
AC + BC + ABC + ABC.
––
––
– ––– – –
ii) ABD + ABC D + ABCD + ABD + A BCD.
(2 marks)
(2 marks)
Minimise the following function using K – map and implement the minimised
function using NAND gates.
f (A, B, C) = ∑ 0,1,2,3,4,5,6
(3 marks)
Implement the following functions using NOR gates having a maximum fan-in
of three.
–
–
––
f = AB + BC D +ABD
(3 marks)
A device accepts numbers in the range 0000 to 1111 that represent 0 to 15. The
output of the circuit is true if the inputs to the circuit represent a prime number
and is false otherwise. Design a circuit using AND, OR and NOT gates to carry out
this function.
(Note: A prime number is an integer that is greater than 1 and is divisible only by
itself and 1. Zero and 1 are not prime numbers)
Describe the functionality of a programmable logic controller (PLC).
Why does a PLC usually have isolation at its digital inputs and outputs?
Suggest and justify two types of isolation that can be used, one for inputs and one
for outputs.
A four-way junction has a basic set of traffic lights with only ‘red’ and ‘green’.
Initially, road A is ‘green’ and road B is ‘red’. The lights stay that way until a vehicle
is detected on road B. The lights then change, so that road A is ‘red’ and road B is
‘green’. The lights stay that way until a vehicle is detected on road ‘A’. The lights
then change to road A ‘green’ and road B ‘red’, and so on.
Draw a flow chart showing the logic of the controller.
Suggest one design to improve the logic of the controller at the road junction.
Explain the functionality of yours.
4
(10 marks)
(2 marks)
(2 marks)
(3 marks)
(10 marks)
(3 marks)
9
a)
b)
c)
Explain the working principle of a thermistor.
Give one reason why it might be preferred as a thermometric device instead of a
platinum resistance thermometer.
Give one reason why a platinum resistance thermometer might be preferred
instead of a thermistor.
(2 marks)
(2 marks)
(2 marks)
Figure Q9a
Figure Q9b
d)
The Figure Q9a shows the resistance of a thermistor in kΩ as a function of
temperature in °C. Two thermistors R1 and R2 of that type are connected in a
circuit as shown in Figure Q9b and are used to measure the difference in
temperature between the environment of R1 and the environment of R2.
Resistors R3 and R4 are 33 kΩ. The supply voltage V is +10 V. You may neglect
the self-heating of the thermistors.
i)
Using the graph, estimate the resistance of R1 at 10 °C and R2 at 20 °C.
Then use your results to calculate the voltage difference at the output.
ii) Repeat your work for R1 at 20 °C and R2 at 30 °C. Calculate the voltage
difference at the output.
iii) How do your results show the suitability of this method for measuring
temperature difference?
5
(5 marks)
(5 marks)
(4 marks)