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THE MANCHESTER METROPOLITAN UNIVERSITY
FACULTY OF SCIENCE AND ENGINEERING
DEPARTMENT OF ENGINEERING AND TECHNOLOGY
SESSION 2004/
Examination for the BEng (HONS) ELECTRICAL AND ELECTRONIC ENGINEERING YEAR ONE
UNIT 64EE1104 : ELECTRICAL ENGINEERING SCIENCE
Wednesday 4 May 2005
9.30 am to 11.30 am
Instructions to Candidates
Answer any FOUR questions.
Breakdown of marks is shown in parentheses.
All questions carry equal marks.
Any type of calculator may be used, but those with non-volatile memory storage facilities must be seen by an invigilator and shown to have been reset immediately before the commencement of the examination.
S121 25/08/
- The circuit shown in Figure Q1 initially has no current and the switch is closed at time t = 0.
Calculate:- (a) the currents i 1 and i 2 immediately after the switch is closed, [2] (b) the maximum possible voltage across the capacitor, [3] (c) the currents i 1 and i 2 when the voltage across the capacitor (vc) is at its maximum value,
[3]
(d) the time constant of the circuit whilst the switch is closed,
[4]
(e) the time taken for the voltage across the capacitor to reach 8V. [5] [Hint: for parts (d) and (e), use Thevenin’s theorem]
The switch is kept closed for a period of 1 second and then opened.
Calculate:- (f) the new time constant, [2] (g) the time taken for the voltage across the capacitor to fall to 4V, [4] (h) the magnitude and direction of the current i 2 at this time. [2]
You may assume that the equations relating the charging and discharging voltage (vc) across a capacitor (C) in series with a resistor (R) are:-
v (^) C = V (1o − e ) v (^) C = V eo
− t − RC
t and RC
where t is the elapsed time and Vo is the final/initial capacitor voltage depending upon whether the capacitor is charging or discharging.
t=
G
iC
20V vc
8.2 kΩ
10 μF^ 10 k^ Ω
i 1 i 2
R 1
R 2
S121 25/08/
- For the a.c. circuit shown in Figure Q2, calculate:
(a) the reactances, (XL2) and (XC1) of the inductor (L 2 ) and capacitor(C 1 ). [4] (b) the impedance of each branch ZS , Z 1 and Z 2 in rectangular and polar form. [4] (c) the total impedance (ZTOT) of the circuit in rectangular and polar form. [6] (d) the currents IS, I 1 , and I 2 in polar form. [8] (e) the total power dissipation. [3]
RS=15Ω R 2 =30 Ω
R 1 =10 Ω
I^ C^1 =100^ μF S
I 1
I 2
240/ 00 V
50 Hz
L 2 =100 mH
Figure Q
continued
- The star connected, balanced 3-phase load of Figure Q4 is supplied from a 400 V, 50 Hz, balanced 3-phase supply.
j9 Ω
I
I
I
R
B
Y
Balanced 3-phase Supply
V BR C
V YB
VRY
V R
j
j V
V
B
Y
C
C
Balance d 3- phase
Figure Q
(a) For the load, determine:- (i) the impedance of each phase in polar form, [3] (ii) all the phase voltages in polar form, (take the phase voltage VR as your reference quantity) [3] (iii) all the line currents in polar form, [4] (iv) the power factor (stating whether lagging or leading), [2] (v) the total power supplied to the 3-phase load. [2]
(b) Draw a phasor diagram showing all phase voltages, line currents and one line voltage. Show clearly how line voltage is constructed. [5]
(c) Three capacitors, of equal capacitance C, are added to the circuit for the purposes of power factor improvement. The capacitors are connected as shown by the dotted lines in Figure Q4. Calculate the required value of C to improve the power factor to 0.9 lagging. [6]
continued
- A shunt excited dc motor is to be connected to a 220 V dc supply for the purposes of driving a pump.
(a) (i) Discuss the main problem which may be encountered in starting such a motor, and suggest one solution. [5] (ii) Describe the effects of armature reaction. [5]
(b) The armature winding resistance is 0.3 Ω and the field winding resistance is 110 Ω and the motor takes a current of 6 A from the dc supply when running on no-load at 1000 rev/min. The motor is now connected to the pump and takes a current of 42 A from the supply, and the effect of armature reaction weakens the field flux by 3%. The mechanical losses of the motor amount to 300 W.
Determine:- (i) the new speed of rotation of the motor, and; [10] (ii) the useful power output. [5]
continued
