DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING
ELECTRICAL & ELECTRONICS FUNDAMENTALS FOR MSC STUDENTS (20 credit) Time allowed 1.5 Hours
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Answer ALL Questions
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Answer ALL Questions
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SECTION A
QUESTION 1
(a) Calculate the rms values of the waveforms shown below.
I(t)
Ip
Ip -Ip
T
I(t)
Ip
T
-Ip
Answers: Ip/√3, Ip and Ip/√2.
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T 2T 3T 4T t I(t)
t
t
(b) Which of the following is NOT a benefit of distributed power generation? POSSIBLE ANSWERS:
T
(1) Reliability & flexibility; (2) Upgradability & economy of scale; (3) Diversity & efficiency; (4) Negligible power integration issues to the central grid.
(c) Which example below is NOT regarded as a distributed power generation type or source? POSSIBLE ANSWERS;
(1) Wind turbine; (2) Solar panel; (3) Local CHP plant; (4) Biomass co-firing with pulverised coal.
[1.5 Marks]
[1.5 Marks]
(d) If the AC voltage waveform shown below is applied to a resistor with resistance R, what is the average power that the said waveform can deliver?
Answer: Vm2/2R.
[3 Marks]
[6 Marks]
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(e) If v1(t)=20cos(t+30o) and v2(t)=30sin(t+70o). Express v(t)=v1(t)+v2(t) as a single sinusoidal function using the phasor approach.
Answer: V = 45.5∠-0.38◦. QUESTION 2
[3 Marks]
[3 Marks]
(a) A voltage defined by 339cos(314t+30o) is applied to a series combination of R = 10 and L = 38mH. (i) What is the rms value of the current flowing?
(ii) What is the current flowing in both phasor and time domain?
Answers: 15.4A, 15.4∠-20◦, i(t) = 21.7cos(314t-20o).
(b) A capacitor of 8 μF takes a current of 1.0A when the alternating voltage applied across it is 250 V. Calculate the following:
(i) The frequency of the applied voltage.
(ii) The resistance to be connected in series with the capacitor to reduce the current in the circuit to 0.5 A at the same frequency.
(iii) The phase angle of the resulting circuit.
Answers: 79.5Hz, 433W and phase angle: 30◦Lead.
[4 Marks]
(c) A coil having a resistance of 6Ω and an inductance of 0.03H is connected across a 50Vrms, 60HZ supply. Calculate the following:
(i) The current.
(ii) The phase angle between the current and the applied voltage. (iii) The apparent power.
(iv) The active power.
Answers: 3.9∠-62◦, -62◦, 195.3 VA, 91.7 VA.
[4 Marks]
QUESTION 3
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In the simplified circuit diagram below, a generator is connected to a load through an overhead line with inductance L (reactance X=ωL) and zero resistance. The indicative phasor diagram for this circuit is also shown below.
VX = IX V1
X =L
V2 Load
Ф
V1
V2 I
Ф
A B
Phasor Diagram
VX = IX
(a) Based upon the relationship in the phasor diagram above show that the term Real Power (P) = (V1V2 sinδ)/X and that Reactive Power (Q) = (V1–V2)V2/X
[4 Marks]
(b) A load is connected to a 50Hz, 1kV generator via a cable that is 100km long and has an inductance of 0.1mH/km. If a real power of 50kW is to be consumed by the load, calculate the following:
(i) The phase difference between the two ends of the line (δ) for operation at the minimum load voltage (90% of the sending end voltage).
(ii) The reactive power consumed and the load power factor for this operating condition.
Answers: δ = 10o, Q = 28.7kVAr and cosθ = 0.867 (29.8o).
[4 Marks]
TOTAL FOR SECTION A [34 MARKS]
SECTION B
QUESTION 4
(a) What is the Laplace transform of 5cos(t)? POSSIBLE ANSWERS:
𝑅(𝑠)
5𝑠2 𝑠2+𝑤2
(1) 𝐻(𝑠) = 5𝑤 ; (2) 𝐻(𝑠) = 5𝑤2 ; (3) 𝐻(𝑠) = 𝑠2+𝑤2 𝑠2+𝑤2
5𝑠 ; (4) 𝐻(𝑠) = 𝑠2+𝑤2
.
(b) What is the closed loop transfer function 𝐶(𝑠) for the control loop in Fig. Q4b below?
[3 Marks]
Fig. Q4b: Feedback control loop.
(1) 𝐶(𝑠) = 𝐺(𝑠) ; (2) 𝐶(𝑠) = 𝐺(𝑠); (3) 𝐶(𝑠) = 𝐺(𝑠) ; (4) 𝐶(𝑠) = 𝐺(𝑠)𝐻(𝑠).
POSSIBLE ANSWERS:
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𝑅(𝑠) 1−𝐺(𝑠)𝐻(𝑠) 𝑅(𝑠) 𝑅(𝑠) 1+𝐺(𝑠)𝐻(𝑠) 𝑅(𝑠)
(c) Based on the step response shown in Fig. Q4c below, this system appears to be:
Fig. Q4c: Step response of system.
POSSIBLE ANSWERS:
(1) critically damped; (2) under damped; (3) ideally damped; (4) over damped.
[3 Marks]
[3 Marks]
√22 2
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QUESTION 5
(a) Which of the following statements is true?
(i) An capacitor stores energy in an electric field.
(ii) Capacitors are primarily used to smooth current.
(iii) Wires have capacitance
(iv) The current through a capacitor stops flowing if it is open circuited.
POSSIBLE ANSWERS:
(1) (i), (iii) and (iv); (2) (i) and (iv); (3) (i), (ii) and (iv); (4) (ii) and (iii).
(b) Consider a 3-phase transmission line whose phase voltages are given by: 𝑉
𝑉 = 𝑉 ∠120∘. What is the magnitude of the line voltage VAB? 𝐶𝑁 𝑝
POSSIBLE ANSWERS:
(1) 𝑣𝑝; (2) √3𝑣𝑝; (3) √3𝑣𝑝; (4) √2𝑣𝑝.
(c) There are three classes of power switching device: uncontrolled devices; controlled devices; and latching devices? Which of the following is a latching device?
POSSIBLE ANSWERS:
(1) Thyristor; (2) MOSFET; (3) Diode; (4) IGBT. [3 Marks]
= 𝑉 ∠0∘, 𝑉
𝐴𝑁 𝑝 𝐵𝑁 𝑝
[3 Marks] = 𝑉 ∠−120∘, and
[3 Marks]
QUESTION 6
(a)
Determine the Laplace transform 𝑣0(𝑠) (without initial conditions) of the transfer function of the circuit in 𝑣(𝑠)
(b)
Using the Final Value Theorem, calculate the steady state error ess of the unity feedback closed loop system in Fig. Q5b for a unity step input. Give your answer with 2 significant digits.
Fig. Q5b: Unity feedback closed loop system.
ANSWER: ess = 0.750 (accept 0.74 to 0.76) [3 Marks]
Consider the circuit in Fig. Q5c. If Vc(0) = 0 V and the capacitor is ideal, answer the following questions:
Fig. Q5c: Circuit for question 5c.
i) What is the magnitude of Vc (in volts) at t = 30 s?
ANSWER: I= 1.5 (accept 1.4 to 1.6) V. [1.5 Marks]
ii) How much energy is stored in the capacitor at t = 90 s ?
ANSWER: Energy = 0 J. [1.5 Marks]
Fig. Q5a:
POSSIBLE ANSWERS: (1) 𝑣0(𝑠) = 1 ; (2)
𝑣0(𝑠) = 𝑣(𝑠)
Fig. Q5a: Circuit for question 5a.
𝑠 ; (3) 𝑣0(𝑠) = 𝑠 ; (4) 𝑣0(𝑠) = 1⁄𝑅𝐶 . [3 Marks] 𝑅𝐶𝑠+1 𝑣(𝑠) 𝑠+𝑅𝐶 𝑣(𝑠) 𝑠+1⁄𝑅𝐶
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𝑣(𝑠) 𝑠+𝑅𝐶
(c)
QUESTION 7
Consider the Bode plot in Fig. Q7 below and answer the following questions:
Fig. Q7: Bode plot of system response for question 7.
(a) How many poles does the transfer function have?
2
ANSWER:
(b) What is the phase margin (in degrees)?
~35 (accept answers between 30 and 40)
POSSIBLE ANSWERS:
(1) 𝐺(𝑠) = 160 𝑠2+8𝑠+16
[1.5 marks]
ANSWER:
(c) Which transfer function best corresponds to the Bode plot in Fig. Q7
; (2) 𝐺(𝑠) =
40 𝑠+4
; (3) 𝐺(𝑠) =
320 ; 𝑠2+2𝑠+16
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[1.5 Marks]
(4) 𝐺(𝑠) = 1 𝑠2+1.5𝑠+16
.
[3 marks]
TOTAL FOR SECTION B [33 MARKS]
SECTION C QUESTION 8
(a) A voltage of 120V is applied to a 4Ω resistor. Calculate the current flowing in the resistor: POSSIBLE ANSWERS:
(1) 3A; (2) 30A; (3) 0.033A; (4) 480A
(b) The gain of an amplifier is 20dB. If the voltage input to this amplifier is 5mV the output would be: POSSIBLE ANSWERS:
(1) 20mV; (2) 100mV; (3) 50mV; (4) 5V
[1.5 Marks]
[1.5 Marks]
POSSIBLE ANSWERS:
(1) 2 ms; (2) 8 ms; (3) 125 s; (4) 500 s
(d) Low pass filtering is related to which mathematical operation? POSSIBLE ANSWERS:
(1) Differentiation; (2) Division; (3) Integration; (4) Multiplication
(e) CMRR stands for: POSSIBLE ANSWERS:
[1.5 Marks]
[1.5 Marks]
Rz y
Figure Q9
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(c) The time constant, τ, of an RC circuit consisting of a resistor with resistance 4kΩ and capacitor with capacitance 2μF is:
(1) Common Mode Reliability Ratio; (2) Common Mode Resistance Ratio; (3) Common Mode Reflection Ratio;
(4) Common Mode Rejection Ratio.
QUESTION 9
[1.5 Marks]
(a) For the circuit shown in Figure Q9, with Rx = 0Ω, Ry = 2.7kΩ and Rz = 47kΩ, calculate the voltage gain of the circuit:
ANSWER:
-17.4 (accept answers from -17.5 to -17.3)
(c) For the circuit shown in Figure Q9, with Rx = 0Ω, Ry = 10kΩ and Rz = 1MΩ, calculate the maximum offset voltage at the output if the input offset voltage has a magnitude of 2mV:
ANSWER in mV:
202 (accept answers from 201 to 203)
(d) For the circuit shown in Figure Q9, with Ry = 0Ω, Ry = 10kΩ and Rz = 1MΩ – the input has an offset current of 100nA – calculate the maximum offset voltage at the output:
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(b) For the circuit shown in Figure Q9, with Rx = 0Ω, Ry = 5.6kΩ and Rz = 56kΩ, calculate the voltage gain in decibels of the circuit in shown:
[4 Marks]
ANSWER in dB:
20 (accept answers from 19.9 to 20.1)
[4 Marks]
[4 Marks]
ANSWER in mV:
ANSWER in Ω:
100 (accept answers from 99 to 101)
(e) For the circuit shown in Figure Q9, with Ry = 10kΩ and Rz = 1MΩ, and with an input offset voltage of magnitude 2mV and a current of 100nA – calculate the value Rx that produces minimal value for the maximum offset voltage at the output:
9901 (accept answers from 9900 to 9902)
(f) For the circuit shown in Figure Q9, with Rx = 0Ω, Ry = 10kΩ and Rz = 100kΩ, and with an input offset voltage of magnitude 1mV and a current of 100nA – calculate the maximum offset voltage at the output:
[4 Marks]
[4 Marks]
ANSWER in mV:
END
[4 Marks]
TOTAL FOR SECTION C [33 MARKS]
21 (accept answers from 20.9 to 21.1)