ELEC1111 – Electrical Circuit Fundamentals
Electrical Circuit Fundamentals
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ELEC1111 – Electrical Circuit Fundamentals
TIME ALLOWED: 160 minutes
TOTAL MARKS: 100
TOTAL NUMBER OF QUESTIONS: 5
THIS EXAM CONTRIBUTES 45% TO THE TOTAL COURSE ASSESSMENT.
Reading time: 10 minutes.
This paper contains 6 pages.
Candidates must ATTEMPT ALL questions.
Answer each question on a separate answer sheet.
Marks for each question are indicated beside the question.
This paper MAY be retained by the candidate.
Print your name, student ID and question number on each answer sheet.
This is an open-book examination. The use of calculators and computers, including
mathematical programs like Matlab, is permitted.
Assumptions made in answering questions should be stated explicitly.
Methods used in answering questions should be described in detail.
Candidates must work alone without any assistance from, or interaction with, other
persons. Any form of academic misconduct may result in failure of the course.
Upload time: 30 min. All answers must be uploaded on Moodle in .pdf, .gif, .jpeg, .png, or
.svg formats no later than 160 min from the time the exam opens.
Page 2 of 6
QUESTION 1 [20 marks]
a. (10 marks) A digital multimeter (DMM) is connected to a resistive circuit as shown
in Figure 1. If the input resistance of the DMM is 1 MΩ, what value will be displayed if
the DMM is measuring voltage (i.e., what is the voltage across the DMM resistance)?
9V
3k
1k
5k
4k 0.7V1
V1+ -
Voltmeter
b. (10 marks) The circuit in Figure 2 represents a solar-powered waste compactor.
During the day, the solar panel charges the battery. When the waste level is lower than
a certain threshold (non-compacting mode), the switch is in position and a bulb is
light up. As soon as the waste level reaches the threshold (compacting mode), the
switch moves to position b, a red LED turns on, and the motor starts compacting waste.
i. (7 marks) What is the voltage across the bulb when the waste compactor is in non-
compacting mode?
ii. (3 marks) Calculate the power dissipated by the battery resistor (i.e., 0.2Ω resistor)
in non-compacting mode.
7A 21 120
0.2
9V 2.5V
380
100
a b
Solar Panel Bulb Battery Red
LED
Motor
Figure 2
Figure 1
Page 3 of 6
QUESTION 2 [20 marks]
a. (10 marks) The switch in the RL circuit shown in Figure 3 was closed for a long time
before opening at = 0 s.
i. (8 marks) Derive the expression for 0() for ≥ 0 s.
ii. (2 marks) Calculate the value of 0 at = 40 ms.
b. (10 marks) The circuit in Figure 4 shows the wiring of the headlights of a car, where
the headlamp bulb has an internal resistance of 2 Ω with an inductance of 75 mH in
series. Due to poor wiring, there is a 5 Ω resistance connected to the headlights circuit.
i. (4 marks) Find the power dissipated by the headlights (both resistor and
inductor) in DC steady state conditions when the switch is closed.
ii. (6 marks) Taking = 0 s as the time when the headlights are first connected (i.e.,
switch closes), derive the expression of the current across the inductor for ≥ 0 .
Consider that the headlights have not been used for a long time and the inductor
is initially discharged.
5
12V
75mH
2
0.5
t = 0s
Car Battery Headlights
Figure 4
Figure 3
20
30
10
30V
0.5H
t = 0s
i0
Page 4 of 6
QUESTION 3 [25 marks]
a. (13 marks) Calculate 0 in the op amp circuit shown in Figure 5.
Figure 5
b. (12 marks) The circuit in Figure 6 represents an audio mixer, where 1 and 2
correspond to individual waveforms from the drums and guitar, respectively. If 1 is a
zero-phase sinusoidal signal with amplitude 240mV, 2 is a zero-phase sinusoidal
signal with amplitude 210mV, and the frequency is 60 ,
i. (5 marks) Derive an expression for the combined phasor voltage 0 in terms of the
input voltages 1 and 2 (i.e., DO NOT substitute the values of 1 and 2).
ii. (2 marks) Substitute the values of 1 and 2 in your calculated 0 from part (i) and
derive the combined waveform 0().
iii. (5 marks) Calculate the average power dissipated by resistor 1 (i.e., 12kΩ
resistor).
v1 v2
C1 = 1µF
C2 = 1µF
R1 = 12k
R2 = 10k
(Drums) (Guitar)
Rf = 10k
v0
+
-
+
Figure 6
0.5V
1k
3k 5k
2k
10k
2k
i0
+
+
Page 5 of 6
QUESTION 4 [23 marks]
a. (12 marks) The circuit shown in Figure 7 is used in a radio receiver to filter a specific
interfering signal. If the amplitude of the input signal is 1V,
i. (5 marks) Derive the expression of the output voltage phasor as a function of
the angular frequency .
ii. (5 marks) Calculate the angular frequency for which the equivalent impedance of
the filter between terminals a-b, Zeq, is purely resistive. Note that this angular
frequency is the frequency of the interfering signal.
iii. (2 marks) Substitute the value of angular frequency obtained in part (ii) in your
derived output voltage phasor from part (i) to find the value of . Based on
this result, explain why the circuit shown in Figure 7 is effectively removing the
interfering signal.
b. (11 marks) Calculate the current 0() in the circuit of Figure 8.
6
i0
-7sin4t V 0.1F 0.1F
6
3V
0.5H
Figure 7
Figure 8
Page 6 of 6
QUESTION 5 [12 marks]
The circuit in Figure 9 represents a household system that allows the operation of 120V, 60
Hz appliances. During winter, the owner wants to connect a heater () to the household
system.
i. (4 marks) Calculate the heater load resistance that will maximize the average
power drawn from the circuit.
ii. (8 marks) Find the maximum average power received by the heater.