AL-LQ-A.C. / p.1
1.
(88-IIB-10)
(a)
Figure (a)
A d.c. electrical circuit includes a conductor in the form of a helical coil which is connected
vertically between two terminals. The lower end of the conductor is not connected tightly but
rests on the lower terminal, making electrical contact with it. When the circuit is switched on, it is
found that current starts and stops periodically and that sparks appear at the lower terminal.
Explain briefly
(b)
(i)
the periodic bursts of current,
(3 marks)
(ii)
the appearance of sparks.
(3 marks)
The rate at which current is switched on and off depends on a number of factors. State one of
these factors.
(1 mark)
(c)
Figure (b)
The coil is then connected in the circuit as shown in Figure (b). The a.c. source is a signal
generator whose output frequency f and r.m.s. voltage V can be varied. As f is changed, V is
adjusted so that the current recorded by the a.c. ammeter is kept constant at 10 mA r.m.s. The
experiment is repeated a number of times, and V
2
is then plotted against
f 2 , as shown in
Figure (c).
Figure (c)
Use the graph to calculate the inductance of the coil.
(3 marks)
AL-LQ-A.C. / p.2
2.
(92-IIB-11)
The figure shows a simplified diagram of a domestic circuit, consisting of an inductor acting as a choke connected
in series with a fluorescent lamp and an a.c. supply. A wattmeter is used to measure the power delivered to the
circuit.
(a)
Why is it important to connect the switch in the live wire?
(2 marks)
(b)
After being switched on, the ammeter in the circuit registers 0.5 A r.m.s. and the wattmeter
indicates that the power delivered to the circuit is 40 W.
(i)
Find the power factor of the circuit.
(2 marks)
(ii)
What is the phase angle between the current in the choke and the p.d. across it? Draw a
phasor diagram to illustrate your answer. (Assume that when the fluorescent lamp conducts,
its resistance is negligible).
(iii) Calculate the resistance and the inductance of the choke.
(c)
(2 marks)
(4 marks)
The household voltage supply in Hong Kong is being changed from 200 V a.c. to 220 V a.c. Give
one reason to support such a change.
(2 marks)
AL-LQ-A.C. / p.3
3.
(93-IIB-10)
A flat circular coil of 100 turns, total resistance 50  and average area 0.01 m2 is placed with its plane
perpendicular to a uniform magnetic field of 0.20 T as shown below.
(a)
The coil is rotated through 180o about a diameter (turned upside down) in the short period of time
of 0.1 s. Calculate, during this period,
(i)
the average e.m.f. induced in the coil;
(3 marks)
(ii)
the average current;
(1 mark)
(iii) the quantity of charge which flows through a cross-section of the wire in the coil. (2 marks)
(b)
Now the coil is being rotated about a diameter at a uniform rate of 5 revolutions per second. Find
(i)
an expression for the current flowing in the coil as a function of time;
(3 marks)
(ii)
the root-mean-square value of the current;
(2 marks)
(iii) the average power dissipated in the coil.
(2 marks)
AL-LQ-A.C. / p.4
4.
(94-I-8)
(a)
(i)
What is meant by the self-inductance of a coil?
(1 mark)
(ii)
A coil usually possesses resistance and inductive reactance in an a.c. circuit. Both quantities
are
measured in ohms (  ). State ONE difference between them.
(1 mark)
(b)
A pure inductor L is connected in series with a 200  resistor R, an ammeter A and a 50 Hz
sinusoidal a.c. supply. (Assume the ammeter and the supply have zero impedance.)
Y1 and Y2 are connected to the two inputs of a dual trace CRO while E is connected to the
common earth connection of the CRO. The graph shows a stable trace pattern obtained on the
CRO screen. Both inputs have the same time-base setting, but their voltage sensitivities are not
the same.
(i)
What is meant by a ‘pure’ inductor?
(ii)
Find the phase difference (  ) between the two traces (
trace leads the other by phase angle
(1 mark)
.
y1 and y 2 ) on the screen. State which
(2 marks)
(iii) Deduce a value for the self-inductance of the inductor L. Show your working clearly by
drawing a phasor diagram.
(3 marks)
(iv) If the ammeter indicates a r.m.s. current of 50 mA, find the r.m.s. voltage of the a.c. supply.
(2 marks)
AL-LQ-A.C. / p.5
5.
(96-I-5)
In the figure below, an a.c. signal generator of constant r.m.s. output voltage is connected in series with
a resistor, R, of resistance 110  , a capacitor, C, of capacitance 4.7  F and an ammeter, A. Both the
signal generator and the ammeter have negligible impedance.
Y1 and Y2 are connected to the two
Y-inputs of a dual trace CRO while E is connected to its common earth connection. The figure below
shows the stable trace pattern,
y 2 , of the voltage across R and C shown on the CRO screen. The
voltage gain and time base for
y 2 are 2.5 Vcm 1 and 2.5 ms cm 1 respectively.
(a)
(i)
What are the peak voltage and the frequency of the applied a.c. signal?
(ii)
Draw a phasor diagram to show the relationship between the applied a.c. voltage, the
voltage across the capacitor and the voltage across the resistor.
(2 marks)
(2 marks)
(iii) Find the phase angle between the applied a.c. voltage and the voltage across the resistor.
(2 marks)
(iv) What is the peak voltage across the resistor?
(v)
Sketch on the above figure the trace pattern of the voltage across R, using the same time
base setting of
(b)
(2 marks)
y 2 but with a voltage gain of 1 Vcm 1 .
(2 marks)
A variable inductor, L, is added to the circuit in the above figure to form an RLC series circuit.
When the inductance of L is gradually increased, the reading of the ammeter A increases to a
maximum and then decreases.
(i)
Explain why the ammeter reading attains a maximum.
(2 marks)
(ii)
Find the value of the inductance of L corresponding to the maximum ammeter reading.
(2 marks)
AL-LQ-A.C. / p.6
6.
(97-I-5)
An iron-cored inductor L, a milliammeter A and a 9 V d.c. supply of negligible internal resistance are
connected as shown in the figure. The graph shows the variation of current with time during the first
few milliseconds, OA, and a few seconds later, BC, after closing switch S.
(a)
What is meant by the inductance of an inductor?
(1 mark)
(b)
(i)
Explain why the current cannot rise instantaneously to the final steady value.
(2 marks)
(ii)
Find the inductance of L.
(2 marks)
(iii) Calculate the resistance of the circuit.
(2 marks)
(iv) If the soft iron core of inductor L is removed, sketch on the same graph the parts
corresponding to OA and BC.
(c)
(2 marks)
When the circuit is broken by opening switch S, sparking occurs at the contacts of the switch.
(i)
Where does the energy for the sparks come from?
(1 mark)
(ii)
In order to prevent sparking, a capacitor is now connected in parallel with the switch. It is
known that sparking occurs when the voltage across the contacts of the switch exceeds 350
V. Assuming that the energy loss due to the resistance of the circuit is negligible, calculate
the minimum capacitance required to prevent sparking.
(3 marks)
AL-LQ-A.C. / p.7
7.
(97-I-6b)
(b)
The figure below shows a simplified tuning circuit for a radio receiver.
(i)
Explain the function of coil L' .
(ii)
Explain how a radio signal of a particular frequency can be picked up by the LC circuit
though radio signals of various frequencies are received by the antenna.
(2 marks)
(2 marks)
(iii) It is preferable to keep the length of the wire for making soil L as short as possible.
Briefly explain why this is so.
(2 marks)
AL-LQ-A.C. / p.8
8.
(97-I-9)
(a)
An operational amplifier of open-loop voltage gain 10 operates with supply voltage  15 V.
What is the voltage across its input terminals when it has just been saturated?
(1 mark)
(b)
(i)
5
In the space provided, draw the circuit of a voltage follower using an ideal operational
amplifier.
(ii)
Explain why, for a voltage follower, the output voltage follows the input voltage exactly.
State one application of such a circuit.
(c)
(2 marks)
(3 marks)
The figure below shows the essential parts of a light-operated alarm circuit. The operational
amplifier in the circuit acts as a voltage comparator so that the LED is on as soon as light is
detected by the LDR. The resistance of the LDR drops from 100 k  to 10 k  in the presence of
light.
(i)
Briefly explain the operation of the circuit.
(3 marks)
(ii)
State the minimum potential at Y for switching on the LED and calculate the minimum
value of the resistance of the 50 k  rheostat below which the circuit will fail to operate.
(3 marks)
AL-LQ-A.C. / p.9
9.
(99-I-8)
(a)
Figure (a) shows an RC circuit constructed form a capacitor C and a resistor R of resistance 5.5 
Figure (a)
(i)
The frequency of the signal generator is slowly increased from zero. Assume that the r.m.s.
output voltage of the signal generator remains constant. Describe the change in ht reading of
the a.c. ammeter A. Briefly explain your answer.
(ii)
(3 marks)
The frequency of the signal generator is set at 2 kHz. Figure (b) shows the traces of VR and
Vo displayed on a CRO.
(I)
(II)
Figure (b)
State the time base used. Use Figure (b) to determine the phase relationship between
VR and Vo.
(4 marks)
Find the r.m.s. values of VR and Vo if the voltage gain used is 5 Vcm-1.
(3 marks)
(III) Calculate the capacitance of C.
(b)
(3 marks)
Figure (c) shows a circuit modified from that in Figure (a). The inductor L has negligible
resistance. Light bulbs X, Y and Z are identical. The frequency of the signal generator is slowly
increased from zero. When the frequency reaches 1 kHz, bulbs X and Y glow with equal
brightness while bulb Z is dim.
Figure (c)
(i)
Describe the change in the brightness of the bulbs X and Y before the frequency of the signal
generator reaches 1 kHz. Explain briefly.
(ii)
(3 marks)
To investigate the voltages across the light bulbs X and Y, the Y-inputs Y1 and Y2 of a dual
trace CRO are connected to P and Q respectively. Sketch the traces displayed on the CRO
when the frequency of the signal generator is 1 kHz and explain why the bulb Z is dim.
(Hint: The sum of currents in X and Y is equal to the current through Z.)
(3 marks)
AL-LQ-A.C. / p.10
10.
(00-I-6)
(a)
Two conductors, a metal rod and a hollow cylindrical conductor, are arranged coaxially. Figure (a) shows
their cross-section. The inner and outer conductors are charged with  Q and  Q respectively, which
is distributed uniformly on their surfaces. Draw the resulting electric field lines.
(1 mark)
Figure (a)
(a)
Figure (b) shows a coaxial cable. The cable consists of an inner conductor, an insulting layer, an outer
conductor and a protective layer.
Figure (b)
(i)
The cable can be represented as conductors AB and A’B’ in a circuit diagram. The cable can be
treated as a capacitor when the inner and outer conductors are taken as the positive and negative
plates. To measure its capacitance per unit length Co, the cable is connected in series with an a.c.
source and a 10 k resistor as shown in Figure (c). The frequency of the source is 100 kHz. The
r.m.s. voltage across the resistor is found to be 1.80 V when that of the source is 2.00 V.
Figure (c)
(I)
Find the r.m.s. voltage across the inner and outer conductors of the cable, that is the voltage
(II)
(ii)
across AA’.
(2 marks)
If the cable is 3.0 m long, find its capacitance per unit length, Co.
(3 marks)
The cable can also be treated as an inductor (single loop) when the inner and outer conductors are
connected (i.e. B is connected to B’).
(I)
The separation between the inner and outer conductors is so small that it is negligible when
compared with the distance from the cable to a point outside it. What is the magnetic field
outside the cable when it is treated as an inductor carrying a current?
(II)
(1 mark)
-7
It is known that the inductance per unit length of the cable, Lo, is of the order 10 Hm-1. With
the 10 k resistor replaced by a 2  one, the circuit in Figure (c) can now be used to
measure Lo. There are two frequencies, 100 kHz and 1 MHz, that can be chosen for the
measurement. Which one is a better choice? Explain briefly.
(2 marks)
AL-LQ-A.C. / p.11
11.
(02-IB-8)
Figure 8.1 shows a circuit consisting of a resistor R and an inductor L connected in series with a
sinusoidal a.c. supply. The supply delivers constant r.m.s. voltage V of variable frequency f and its
internal impedance is negligible. When f is set to 100Hz, the peak current in the circuit is 50mA.
The figure on the graph paper is a phasor diagram (drawn to scale) for the circuit. Line AB represents
the peak voltage across L, AC the peak voltage of the supply and AD the peak voltage drop across R.
(a)
(i)
What feature of the phasor diagram indicates that L is not a ‘pure’ inductor?
(ii)
What is the peak voltage of the a.c. supply?
(iii)
Find the resistance of the resistance R.
(iv)
Calculate the resistance and inductance of the inductor L.
(v)
Calculate the power factor of this circuit. Give its physical meaning and state in what way
it is affected by the frequency of the supply.
(b)
Figure 8.2 shows the variation of the potential VX at point X in the circuit against time t. On the
same figure, add a graph to show the variation of the potential VY at Y against time t.
(c)
If the frequency f is increased from a small value, sketch a graph to show how each of the
following varies with f.
12.
(i)
the peak current I in circuit.
(ii)
The peak voltage VL across the inductor
(04-IA-4)
(a)
A high-pitch note of frequency 4kHz is amplified to a r.m.s. voltage of 4 V and the output is fed to a tweeter
(high frequency speaker) circuit is shown in Figure 4.1. The capacitance of the capacitor C is 50 F.
Assume that the tweeter can be regarded as a resistor R of resistance 8.
Figure 4.1
(i)
Find the impedance between A and B to 3 significant figures. (3 marks)
(ii)
Find the r.m.s. current passing through the tweeter. Hence, calculate the average power consumption
of the tweeter when the notes is being played. (3 marks)
(b) A low-pitch note of frequency 80 Hz is also amplified to a r.m.s. voltage of 4 V and the output is fed to the
tweeter current in Figure 4.1.
(i)
Find the phase difference between the current passing through the tweeter and the voltage across AB.
Draw a phasor diagram to represent their relationship. (3 marks)
(ii)
Find the average power consumption of the tweeter in this case. (2 marks)
(c) The two notes no sound together at 80Hz and 4 kHz respectively. They are both amplified to the same r.m.s.
voltage and the output is fed to a 2-way speaker, which consists of a woofer (low frequency speaker) and a
tweeter crossover network as shown in Figure 4.2. Assume that the woofer can also be regarded as a resistor
R of resistance 8.
AL-LQ-A.C. / p.12
Figure 4.2
The function of component X is to block high frequency signals. Suggest what component X should be and
explain how it works. (3 marks)