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THE MANCHESTER METROPOLITAN UNIVERSITY
FACULTY OF SCIENCE AND ENGINEERING
DEPARTMENT OF ENGINEERING AND TECHNOLOGY
SESSION 2002/
Examination for the BEng (HONS) ELECTRICAL AND ELECTRONIC ENGINEERING (FULL-TIME/SANDWICH) YEAR ONE
UNIT 64EE1104 : ELECTRICAL ENGINEERING SCIENCE
Thursday 8 May 2003
2.00 pm to 4.00 pm
Instructions to Candidates
Attempt ANY FOUR questions. Breakdown of marks for each question is shown in square parentheses.
Students are permitted to use their own calculators subject to Faculty conditions. Alpha-numeric memories must be cleared prior to the start of the examination.
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- 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 10V. [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
16V vc
2kΩ
(^5) μF 6kΩ
i 1 i 2
R 1
R 2
Figure Q
- An oscilloscope is used to display the waveforms of the two voltages as shown in Figure Q3. It is known that there is no dc offset voltage for either of the two waveforms, and that the lower trace is a full-wave rectified sinewave. The settings of the oscilloscope are as follows:-
Y1 amplifier (upper trace) 1 V/div Y2 amplifier (lower trace) 5 V/div Timebase 0.5 ms/div
From the oscilloscope measurements and for each waveform, determine:
(a) the peak voltage; [2]
(b) the time period; [3]
(c) the frequency. [3]
In addition, confirm ONE average and ONE r.m.s. value of the waveforms given in the following table:-
Y1 (Upper Trace) Y2 (Lower Trace) (d) Average Voltage (V) 0.75 6. (e) R.M.S. Voltage (V) 1.22 7.07 (^) [ 10 ]
[ 7 ]
Figure Q
- The star connected, balanced 3-phase load of Figure Q4 is supplied from a 415 V, 50 Hz, balanced 3-phase supply.
j (^12) Ω
I
I
I
R
B
Y
Balanced
3-phase
Supply
V BR C
V YB
VRY
V R
j 12
j 12 V
V
B
Y
C
C
Balanced 3-phase load
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]
- (a) Define Electric Field Strength (E) and state clearly the units in which it is measured. [5]
(b) Figure Q6.1 shows two point charges A and B, situated in air.
(i) Determine the magnitude and direction of the Electric Field Strength (E) at the point P. (You may assume that εo = 8.85 × 10 -12^ F/m) [6]
(ii) For a charge of 5μC at B, find the value of the charge at A which would reduce the field strength at P to zero [6]
2 μ C 0.15 m 0.2 m^5 μC
A P B
Figure Q6.
(c) A parallel plate capacitor is filled with two different insulating materials of equal thickness and relative permittivity ε 1 and ε 2 as shown in Figure Q6. Show that the total capacitance, C is given by:-
1 +^2
0 1 2 ε ε
εε d
2 εA C = ε 1 ε 2
d
Area A
Figure Q6.
[8]
END
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