HKAL Extra Exercise : Part 4 Electricity and Electromagnetism
Chapter 15 Electric Circuits
15.1 Electric Current : Drift Velocity
1. An electric current is flowing in a copper wire which is part of a circuit. The electrons in the
copper wire
A. had random motion onto which was imposed a drift velocity of a few millimetres per
second when the switch was closed.
B. were at rest until the switch was closed but now moved along the wire with a drift
velocity of a few millimetres per second.
C. had random motion until the switch was closed but now moved along the wire at a
speed approaching the speed of light.
D.
had random motion onto which was imposed a drift velocity of a few kilometres per
second when the switch was closed.
2.
If a metal conductor, of cross-sectional area A, has n free electrons per unit volume, each
carrying a charge e and moving with a drift velocity v, the
(1) current density will be nevA.
(2) current flow will be evA.
(3) drift velocity will increase with the applied voltage.
A. (1) only
B. (3) only
C. (1) and (2) only
D. (1), (2) and (3)
3.
Which of the following quantities remain unchanged by increasing the voltage across a metal
wire ?
(1) the speed of the electrical signal
(2) the current density
(3) the average drift velocity of the conduction electrons
A. (1) only
B. (3) only
C. (1) and (2) only
D. (2) and (3) only
4.
A resistance wire is connected across the terminals of a battery. Which of the following
statements is correct ?
A. Before connection to the battery, the conduction electrons in the wire were at rest.
B.
C.
D.
The conduction electrons in the wire are accelerated momentarily along the direction
to that of the electric field.
The current in the wire is inversely proportional to the average drift velocity of the
electrons.
After connection to the battery, a potential difference is set up along the length of the
wire.
HKAL Extra Exercise Chapter 15 Electric Circuits
1/14
15.2 Electromotive Force : Definition
5. The e.m.f. of a battery is equal to
(1) the total electrical power it generates divided by the current it delivers.
(2) the potential difference across its terminals when it is on open circuit.
(3) the total electrical power it releases, per coulomb of charge when connected to an external
circuit.
A. (1) only
B. (3) only
C. (1) and (2) only
D. (1), (2) and (3)
15.3 Resistance
6.
8.
5 V, 2 
6
Y
X
1A
Y
X
The figure above shows part of a circuit
which carries a current of 1 A from X to Y
through a cell of e.m.f. 5 V and internal
resistance 2 Ω. The potential difference
In the above circuit, X and Y are identical
cells, of e.m.f. 20 V and internal resistance
8 Ω. What is the current passing through
the 6 Ω resistor?
A.
B.
C.
D.
1A
10/7 A
2A
20/7 A
between X and Y is
A. 2 V.
C. 5 V.
B.
D.
3 V.
7 V.
Dependence of Resistance
9.
7.
current/A
6V
A
6.0
V
K
4.0
100 
In the above circuit, V is a voltmeter of
high internal resistance and A is an
ammeter of low internal resistance. What
is the voltmeter reading when (a) switch K
is open, (b) switch K is closed ?
K open K closed
A.
0V
3V
B.
0V
6V
C.
6V
3V
D.
6V
6V
HKAL Extra Exercise Chapter 15 Electric Circuits
0
1.0
2.0 voltage/V
The variation of current with the voltage
applied across a device is as shown. What
is the change in resistance of the device
when the voltage increases from 1.0 V to
2.0 V ?
A. It increases by 1.0 Ω
B. It decreases by 1.0 Ω
C. It increases by 0.1 Ω
D. It decreases by 0.1 Ω
2/14
Internal Resistance of Battery
10. A d.c. supply of constant e.m.f. and
internal resistance is connected to a
variable resistor of resistance R. Which of
the following graphs best shows how the
voltage V delivered by the supply varies
with R ?
A.
B.
V
0
0
C.
D.
V
V
0
R
0
12.
internal resistance 5 
V
R
the internal resistance of the cell ?
A. 1.92 Ω
B. 0.88 Ω
C. 0.58 Ω
D. 0.15 Ω
R
R
In the above circuit, the internal resistance
of the battery is 5 Ω. R is a variable
resistor. Which of the following statements
about the circuit is/are correct ?
(1) If the resistance of R is 5 Ω, the
R
voltage supplied to R by the battery is
at a maximum.
11.
A
A cell of e.m.f. 1.4 V is connected in
series with a variable resistor of resistance
R and an ammeter A of resistance 0.3 Ω.
By varying R, a series of ammeter
readings, I, are taken and a graph of
1
I
against R is plotted. The value of the
y-intercept is found to be 0.63 A-1. What is
HKAL Extra Exercise Chapter 15 Electric Circuits
(2) If the resistance of R is very small,
the current in the circuit is very large
and the power dissipated in the
battery is large.
(3) If the resistance of R is very large, the
terminal potential difference of the
battery is very large but the power
dissipated in the battery is small.
A. (1) only
B. (3) only
C.
D.
(2) and (3) only
(1), (2) and (3)
3/14
Combination of Resistors
13.
16 
16 
16 
X
16 
Y
16 
16.
16 
16 
16 
In the circuit above, the equivalent
resistance across XY is
A. 80 Ω.
B. 40 Ω.
C. 20 Ω.
D. 0 Ω.
3
2
2
B
3
In the above circuit, the equivalent
resistance between A and B is
A. 2 Ω.
B. 8/5 Ω.
C. 6/7 Ω.
D. 3/5 Ω.
15.
9
9
80 
C
50 
B
R
80 
D
The above figure shows a network of
resistors. If a voltage 180 V is applied
across terminals A and B, the potential
difference between C and D is 30 V. If the
voltage is applied across terminals C and
D instead, what is the potential difference
between A and B ?
A. 25 V
B. 20 V
C. 5 V
D. It cannot be found as the value
of R is not known.
14.
A
50 
A
9
I
2V
In the above circuit, the battery has
negligible internal resistance. The current I
is
A. 2/27 A.
B. 2/9 A.
C. 2/3 A.
D. 1 A.
HKAL Extra Exercise Chapter 15 Electric Circuits
17. A 20 V, 10 W light bulb in a set of
Christmas tree lights (which consists of 20
bulbs in series) burns out and Jimmy goes
to buy a replacement. When he gets back,
he finds that although the new bulb is
marked 10 W, the light it gives is very
bright, although the other bulbs light up
brightly. Which of the following is a
possible reason for this?
(1) The supply voltage has raised above
400 V.
(2) The bulb is designed to work at a
voltage lower than 20 V.
(3) The current through the circuit is
very much larger than 0.5 A.
A. (1) only
B. (2) only
C. (1) and (2) only
D. (1), (2) and (3)
4/14
18.
21
6V
X
R
1.1 A
1.1 A
9
G
10 
24 Ω
G
Y 3
D.
Two cells X and Y, each of internal
resistance 3 Ω, are connected with two 9
Ω resistors as shown in the above circuit.
If cell X has e.m.f. 6 V and the
46 Ω
galvanometer G shows null deflection,
what is the e.m.f. of cell Y ?
A. 11 V
B. 12 V
C. 14 V
D. 42 V
19
24 V
X
12 
9
20 
In the circuit shown , no current flows
through the galvanometer G. If the internal
resistance of the cell is negligible, what is
the value of R?
A. 5.5 Ω
B. 6.7 Ω
C.
6 V, 3 
8
22
S
Y
Q
2V
V
6
A high resistance voltmeter is connected
between points X and Y in the circuit
shown. When the switch S is open, the
reading on the voltmeter is approximately
A. 0 V.
B. 5 V.
C. 14.4 V.
D. 24 V.
4
P
Two cells of negligible internal resistance
are connected with two resistors as shown.
What is the potential difference between P
and Q ?
A. 2.8 V
B. 4.8 V
C. 5.2 V
D. 7.2 V
20
X
G
12 V
4V
50 
In the circuit shown above, the
galvanometer G reading is zero. So X has
a resistance of
A. 25 Ω.
B. 50 Ω.
C. 100 Ω.
D. 150 Ω.
10 V
23
G
12 V
1 k
E
2 k
3 k
In the above circuit, the galvanometer
HKAL Extra Exercise Chapter 15 Electric Circuits
5/14
reading is zero. If both cells have
negligible internal resistance, the e.m.f. of
the cell E is
A. 3 V.
C. 6 V.
26
12 k
B.
D.
4 V.
9 V.
8V
V
voltmeter, 3 k
24 Six wires, each of resistance 2 Ω, are
joined to form a regular tetrahedron ABCD.
A current of 1 A flows across the
tetrahedron at A and B.
C
In the above circuit each cell has
negligible internal resistance. The
voltmeter has a resistance of 3 kΩ. The
1A
reading on the voltmeter is
B
1A
A
C.
D.
A.
C.
D
Which of the following statements is/are
correct ?
(1) The current in wire AD is 0.5 A.
(2) The potential drop across AB is 0 V.
(3) No current flow through wire CD.
A. (1) only
B. (3) only
B.
D.
1.4 V.
0 V.
S
V
In the above circuit, the resistors are
identical, the battery has negligible
internal resistance and the voltmeter draws
negligible current. What are the possible
voltmeter readings before and after closing
switch S ?
S open
S closed
A.
3V
2V
B.
3V
1V
C.
1V
3V
D.
1V
2V
25
L2
L1
L3
HKAL Extra Exercise Chapter 15 Electric Circuits
2 V.
1 V.
27
(1) and (2) only
(2) and (3) only
In the above circuit, light bulbs L1 , L2 and
L3 consume power at the rate 1 : 5 : 1. If
the resistance of L2 is R, the resistance of
L1 is
A. 5R/36.
B. 5R/7.
C. 5R/6.
D. 5R.
6V
9 k
28
R1
P
Q R
3
S
R2
6/14
In the above circuit, the battery has
constant e.m.f. and negligible internal
of V3 and the potential difference across
resistor R.
resistance. If switch S is closed, what
would happen to the electric potential at P
and at Q ?
Potential at P Potential at Q
A. increased
increased
B. increased
decreased
C. decreased
increased
D. decreased
decreased
Voltmeter
Potential
Reading of V3 difference across R
5V
1V
3V
1V
1V
3V
1V
5V
A.
B.
C.
D.
31
36 V
29
1
48 
48 
2
0.6 A
0.2 A 5 
S
R
L1
L2
The figure shows some of the resistors in a
network of resistors. The magnitudes and
directions of some of the currents are
marked as shown. Find the magnitude and
direction of the current passing through
In the circuit shown, filament lamps L1
and L2 are identical and are seen to be
marked ‘12 V 24 W’. Which of the
following statements is/are correct ?
(1) When switch S is closed, lamp L2
the resistor R.
A. 0.5 A from left to right
B. 1.0 A from left to right
C. 0.5 A from right to left
D. 1.0 A from right to left
glows with its normal brightness.
(2) When switch S is opened, lamp L1
glows with its normal brightness.
(3) When switch S is closed, lamp L1 and
lamp L2 glow with the same
brightness.
A. (1) only
B. (3) only
C. (1) and (2) only
D. (2) and (3) only
30
12 V
R
S
V3
V1
V2
In the above circuit, the d.c. supply has an
e.m.f. of 12 V and its internal resistance is
negligible. V1, V2 and V3 are three
voltmeters with the same finite internal
resistance. If V1 reads 4 V, find the reading
HKAL Extra Exercise Chapter 15 Electric Circuits
32 X and Y are bulbs with ratings ‘4 V, 8 W’
and ‘8 V, 8 W’ respectively. If they are
connected to a 12 V supply of negligible
internal resistance, which of the following
connections allows the two bulbs to work
at their respective rated values ?
7/14
A.
B.
C.
D.
X
X
Y
X
Y
Y
Y
X
15.4 Power and Heating Effect
33 Only a small fraction of the electrical
energy supplied to a light bulb is
converted into light energy. Which of the
following explanations is/are correct ?
(1) Joule heating of the filament.
(2) The resistance of the filament of the
bulb is very high.
(3) Most of the energy is emitted as
infra-red radiation.
A. (1) only
B. (3) only
C. (1) and (2) only
D. (1), (2) and (3)
34
with armature resistance 3 Ω . If the
ammeter A of negligible internal resistance
shows a reading of 0.3 A, the maximum
useful output power delivered by the
motor is
A. 0.3 W.
B. 1.2 W.
C.
3.3 W.
D.
3.6 W.
36 Two cylindrical metal rods, X and Y, are
made from the same material and have the
same mass. The length of X is five times
that of Y. If currents of 1 A and 6 A pass
through X and Y respectively, the ratio of
the power dissipation in X to that in Y is
A. 25 : 36
B. 6 : 5
C. 5 : 6
D. 5 : 36
R1 = 2 
Y
X
37
R2 = 1 
In the circuit above, an electron traveling
from Y to X through R1 loses energy E1,
and an electron traveling from Y to X
through R2 loses energy E2. E1 is equal to
A. E2/3.
B. E2/2.
C. E2.
D. 2E2.
35
A
12 V
A 12 V battery of negligible internal
resistance is applied to a d.c. motor M
HKAL Extra Exercise Chapter 15 Electric Circuits
+
4V
Q
P
J
L1
L2
In the above circuit, PQ is a uniform
resistance wire connected to a 4 V
constant voltage source. L1 and L2 are two
identical light bulbs, each of rating 16 V,
64 W. What is the power dissipated by L1
when the sliding contact J is at the
mid-point of PQ ?
A. 1 W
B. 8 W
C. 64 W
D. 4094 W
8/14
38 Three resistors of resistance R1, R2 and R3 are connected in series. It is known that R1 > R2 >
R3 . The equivalent resistance of this combination is R. Which of the following statements
is/are correct ?
(1) R is larger than R1.
(2) If the resistor with resistance R1 is shorted, the resulting equivalent resistance is increased.
(3) Energy dissipated in moving 1 C of charge through the resistor of resistance R1 is greater
than that through R3.
A. (1) only
B. (1) and (3) only
C. (2) and (3) only
D. (1), (2) and (3)
Power output and Resistance
39. A steadily running motor draws a current of 1 A from a battery of e.m.f. 8 V. The internal
resistance of the battery is negligible. If the resistance of its armature coil is 3.0 Ω, estimate
the efficiency of the motor.
A. 27%
B. 37%
C. 63%
D. 73%
Power Transmission
40. A power station supplies electrical power
42.
to a user. The power generated by the
station is 1 500 kW and is transmitted at
factory
generator
machines
112 000 V. If the resistance of the lines
connecting the power station to the user is
350 Ω, the power available to the user is
The machines in a factory consume 30 kW
about
of electrical power at a voltage of 800 V. If
A.
B.
C.
D.
1 437 kW.
1 494 kW.
1 500 kW.
35 840 kW.
41. Electrical power is transmitted at high
voltage over long distances because
(1) a larger amount of energy can be
transmitted per unit charge.
(2) the energy can be transmitted in a
faster speed.
(3) a smaller current is required for a
fixed amount of power delivered.
A. (3) only
B. (1) and (2) only
C. (1) and (3) only
D. (1), (2) and (3)
HKAL Extra Exercise Chapter 15 Electric Circuits
the generator is connected to the factory
through cables of total resistance 0.4 Ω,
the e.m.f. produced by the generator
should be
A. 801 V.
B. 802 V.
C. 812 V.
D. 820 V.
Domestic Electricity
43. Which of the following is/are equivalent
to a unit energy ?
(1) volt-ampere
(2) kilowatt-hour
(3) ampere-ohm
A. (2) only
B. (3) only
C. (1) and (2) only
D. (1), (2) and (3)
9/14
Bridge Circuits (Wheatstone Bridge)
44.
(1) The current across R is equal to the
potential difference across S.
(2) P/S = Q/R
(3) S(Q + R) = R(P + S)
A. (2) only
B. (3) only
C. (1) and (2) only
D. (2) and (3) only
P
X
G
Q
R
The diagram shows a Wheatstone bridge
circuit, P, Q and R are resistance boxes
whose resistance may be set at zero or any
integral number of ohms, up to 1 500. X is
an unknown resistance to be measured by
adjusting R. With P and Q each set at 100
ohms, it is not possible to balance the
bridge, and the current through the
galvanometer is always in the same
direction. Which one of the following
explanations could account for this
failure ?
A.
B.
C.
D.
X is greater than 1 500 ohms.
X is greater than 800 ohms.
X is greater than 200 ohms.
X is greater than 100 ohms.
45.
S
P
G
Q
R
46.
x
S
P
G
Q
R
y
The figure above shows 4 resistors, of
resistance P, Q, R and S in a Wheatstone
bridge circuit. Which of the following
statements is/are correct when the bridge
is balanced ?
(1) The current through G will still be
zero when the battery and the
galvanometer are interchanged.
(2) The p.d. across P is equal to the p.d.
across S.
(3) The potential at point x is equal to the
potential at point y.
A. (1) only
B.
C.
D.
(1) and (3) only
(2) and (3) only
(1), (2) and (3)
The figure above shows 4 resistors, of
resistance P, Q, R and S in a Wheatstone
Bridge circuit. Which of the following
statements is/are correct when the bridge
is balanced?
HKAL Extra Exercise Chapter 15 Electric Circuits
10/14
47.
V and negligible internal resistance. The
resistance of the four resistors R1, R2, R3
and R4 are 5 Ω, 2 Ω, 1 Ω and 4 Ω
A
R1
R2
C
respectively.
The
capacitor
has
capacitance 21μF. At steady state, the
R3
R4
charge on the capacitor plate connecting to
A is
A. +63μC
B. +162μC
C. -63μC
D. -162μC
B
21 V
In the above circuit, the cell has e.m.f. 21
15.5 Measuring Devices
Potentiometer
The potentiometer circuit shown is used to find
48.
E1
R1
P
X
Y
E2 G
R2
The diagram shows a potentiometer circuit.
Which of the following statements is/are
INCORRECT ?
(1) If R1 is increased, the balance point P
will be unchanged.
(2) If R2 is increased, the balance point P
will be unchanged.
(3) If the e.m.f. E2 raises, the balance
point P will be unchanged.
A. (1) only
B. (1) and (2) only
C. (2) and (3) only
D. (1), (2) and (3)
49.
V
T
P
R
Q
G
the internal resistance of the cell E. At balance,
the galvanometer pointer does not deflect, and
there is current flows through
(1) the galvanometer G.
(2) the battery E.
(3) the battery V.
A. (1) only
B. (1) and (2) only
C. (2) and (3) only
D. (1), (2) and (3)
50.
X
R
C
A
Y
B
G
In the above circuit, C denotes the balance
position on the potentiometer wire AB. Which
of the following procedures can shift C towards
the end A?
(1) adding a resistance in series with the
galvanometer G.
(2) replacing the driving cell X by one with a
larger e.m.f.
(3) replacing the cell Y by a cell with a
smaller emf.
A. (1) only
B. (3) only
C. (1) and (2) only
D. (2) and (3) only
E
HKAL Extra Exercise Chapter 15 Electric Circuits
11/14
51.
A.
S
B
Z
X
3V
3V
Y
A
R
B
C.
V
In a potentiometer experiment, a balance
point was found on the potentiometer wire
XY at Z. After switch S had remained
closed for some time, it was found that the
contact at Z had to be moved towards X to
maintain the balance. The most likely
reason was that
A. R was getting warm and its
resistance was increasing.
B. the galvanometer coil was
getting warm and its resistance
was increasing.
C. the cell B was running down.
D. the cell V was running down.
B
3V
A
B
A
B
53.
B
X
Y
4
A
The above potentiometer circuit is used to
calibrate an ammeter A. XY is the
potentiometer wire and the potential drop
across the wire is 0.02 V/cm. B is the
balance point and XB = 45 cm. The current
passing through the ammeter A is
A. 0.2 A.
B. 0.8 A.
C. 0.9 A.
D. 3.6 A.
V
1
S
A
D.
3V
52.
A
B.
B
54.
3V
20 V
In the above figure, AB is a resistance wire
of uniform cross-section, and S is a sliding
contact. The 3 V battery has negligible
internal resistance, and V is a high
resistance voltmeter. Which of the
following graphs shows the correct
variation of voltage measured by V when
the contact S is moved from A to B ?
HKAL Extra Exercise Chapter 15 Electric Circuits
A
X
B
10 
In the above circuit, AB is a metre-wire of
resistance 40 Ω. When X is moved to the
mid-point of AB, the p.d. across AX will be
A. 4 V.
B. 5 V.
C. 15 V.
D. 16 V.
12/14
55.
57.
15 cm
E
C
A
S
R
50 cm 70 cm
uniform resistance
wire carrying
steady current
B
G
G
20 
X
In the potentiometer circuit shown, S is a
source whose e.m.f. is to be measured. R is a
resistor to protect the galvanometer G. In the
experiment, a student finds that G deflects in
the same direction for any position of C, giving
maximum deflection at B and minimum
deflection (not zero) at A. Which of the
following is the possible reason?
A. The e.m.f. of the driver cell E is too low.
B. The driver cell E has a large internal
resistance.
C. S is connected with wrong polarity.
D. There is contact resistance at A and B.
In the above circuit, the galvanometer G
reads zero. The resistance of resistor X is
A. 20 × (4/7) Ω
B. 20 × (5/7) Ω
C. 20 × (7/4) Ω
D. 20 × (7/5) Ω
Measuring very small p.d.
58.
B
R
S
P
Q
G
56.
X
E1
R1
X
P
A
E2
R2
Q
G galvanometer
B
The figure above shows a potentiometer circuit
used for measuring the e.m.f.s of cells. The
potential gradient along the potentiometer wire
PQ is assumed to be constant. Which of the
following statements is/are true ?
(1) If the balance point X is close to P, the
resistance R1 should be decreased.
(2) At balance, there is no current flowing
through the path PXQ.
(3) At balance, it is better to have point X near
Q.
A. (2) only
B. (3) only
C. (1) and (2) only
D. (1) and (3) only
HKAL Extra Exercise Chapter 15 Electric Circuits
Y
The potentiometer circuit above was set
up to determine the e.m.f. of a
thermocouple XY. PQ is a uniform
resistance wire. As the sliding contact S is
moved along PQ towards Q, the
galvanometer
deflection
decreases
continuously in the same direction, but
does not become zero. Which of the
following is NOT a possible reason ?
A. The e.m.f. of the thermocouple
B.
C.
D.
is too large.
The e.m.f. of the thermocouple
has a wrong polarity.
The resistance R is too large.
The galvanometer resistance is
too small.
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Ammeter and Voltmeter
59. A meter has a scale marked –20μA to
A.
B.
+100μA and its resistance is 20 Ω. In
order to convert it to a voltmeter with a
positive full-scale deflection of +10 mV, it
is necessary to add a resistance R
A. in parallel, R = 0.2 Ω
B. in parallel, R = 80 Ω
C. in series, R = 0.2 Ω
D. in series, R = 80 Ω
+
-
R
A
+
-
R
A
+
V
C.
V
-
D.
R
A
+
60.
+
V
R
A
V
-
99.9 k
3
9.9 k
2
1
P
62.
100 
3
0.1001  2 Q
1.01 
1
input
terminal
The diagram shows the circuit of a
multimeter with ranges 0 – 0.1 A, 0 – 1 A,
0 – 10 V and 0 – 100 V. What must be the
positions of the range switches P and Q if
the current to be measured is about 45 V?
P Q
P Q
A. 2
1
B. 2
2
C. 3
2
D. 3
3
61. Which of the following circuits is best
used for the measurement of a high
resistance R?
(Polarities of meter terminals are given in
the diagram.)
KEY :
V
A
R
The above circuit can be used to find the
resistance of the resistor R. Which of the
following statements is/are correct ?
(1) The voltage across the voltmeter is in
fact larger than that across R.
(2) The ratio of voltmeter reading to
ammeter reading is in fact larger than
the resistance of R.
(3) The circuit is suitable for measuring
high resistance.
A. (3) only
B. (1) and (2) only
C.
D.
(2) and (3) only
(1), (2) and (3)
1 – 10 : DBABC, CDBBB, 11 – 20 : CCCDC, BBCCC, 21 – 30 : CCABA, DCAAC,
31 – 40 : DABCC, AABCA, 41 – 50 : CDAAA, BDDCD, 51 – 60 : DBABC, BCDDD,
61 – 62 : DD.
HKAL Extra Exercise Chapter 15 Electric Circuits
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