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HKAL Extra Exercise : Part 4 Electricity and Electromagnetism
Chapter 14 Capacitance
14.1 Capacitance
1.
A potential difference V is applied between two large parallel plates, distance s apart. An
electron, mass m, charge –e, starts from rest at the negative plate and travels across the gap to
the positive plate. Its final speed is
m
A.
.
2e V
B.
2e V
.
2ms 2
.
eV
C.
m
D.
eV
.
ms
2.
B
A
+
P
x
-
s
The figure above shows a charged parallel plate capacitor. P is a point between the plates and
its distance from plate A is x. If V is the electric potential at point P, which of the following
graphs best represents the variation of V with x? (The separation of the plates is s.)
A.
B.
C.
D.
V
0
V
s
x
0
V
s
x
0
V
s
x
s
0
x
Capacitance of Two parallel Plates
3.
A parallel-plate capacitor is formed by two circular metal plates. To determine the capacitance
C, a student measures the radius r and separation d of the plates.
If the maximum percentage error of r = 7%,
the maximum percentage error of d = 3%,
then the maximum percentage error for C will be
A. 7%
B. 10%
C. 13%
4.
D.
17%
If the length of the sides of the square plates of a parallel-plate capacitor is decreased by 25%,
its capacitance will
A. decrease by 25%.
B. decrease by 56%.
C. increase by 33%.
D. increase by 33%.
HKAL Extra Exercise Chapter 14 Capacitance
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5.
6.
P
Q
In the capacitor arrangement shown in the
diagram, plate P has been charged and
connected to the electroscope. If plate Q is
moved upward from plate P, the gold-leaf
will
A.
B.
C.
D.
remain where it is.
diverge a lot more.
diverge a little more.
fall slightly.
A parallel-plate capacitor is first charged by
connecting it to a battery. After disconnecting
the battery, one of the plates of the capacitor is
shifted toward the other plate as shown. What
would happen to each of the following
quantities ?
V : the potential difference between the plates
Q : the magnitude of the charge on each plate
C : the capacitance of the capacitor
V
Q
C
A. increased
unchanged increased
B. unchanged decreased
decreased
C. decreased
decreased
decreased
D. decreased
unchanged
increased
Capacitors with Dielectric
7. C1 and C2 are plane parallel plate
plates. Neglecting edge effects, the electric
capacitors of the same area. The plates of
C1 and C2 are separated by slabs of the
same dielectric material of thickness d and
5d respectively. The capacitance of C1 is
0.24μF. The capacitance of C1 and C2
connected together in series is
A. 0.04μF.
B. 0.05μF.
C. 0.20μF.
D. 0.29μF.
8.
field strength at Q when the capacitor is
charged is
A. the same as that at P.
B. equal in magnitude but opposite
in direction to that at P.
C. less than that at P.
D. greater than that at P.
9.
-
+
Q
A
M
B
P
A sheet of dielectric occupies part of the
space between the parallel of an evacuated
capacitor. P is a point in the dielectric and
Q is a point in the vacuum between the
HKAL Extra Exercise Chapter 14 Capacitance
Two large metal plates A, B are oppositely
charged and placed a small distance apart.
A piece of metal M is placed centrally
between the plates. Which of the
following graphs shows the variation of
electric potential V from A to B ?
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A.
B.
C.
D.
V
V
V
V
A
B
A
B
A
B
A
B
14.2 Combination of capacitors : Equivalent Capacitance
10. A parallel-plate capacitor of capacitance
C0 is formed by two rectangular metal
plates having separation d. Now each of
12.
X
the plates is cut into five smaller, identical
ones to form two capacitors, each with
plate separation 5d. What is the
capacitance when they are connected in
parallel ?
A. (1/50)C0
B. (2/25)C0
C. (1/10)C0
D. (2/5)C0
11. Which one of the following combinations
has the greatest capacitance?
A.
Y
Three identical capacitors, each of
capacitance C, form a network as shown.
What is the equivalent capacitance
between terminals X and Y ?
A.
1
C
3
B.
2
C
3
C.
C
D.
3C
13.
C
C
0.50 F
0.25 F
C
0.20 F
B.
d. c. source
0.20 F
C.
0.50 F
0.25 F
0.20 F
D.
0.20 F
0.50 F
C
C
0.50 F
0.25 F
C
d. c. source
Circuit A
Circuit B
Three identical capacitors are connected to
the same d.c. source in series (circuit A)
and then in parallel (circuit B). The
magnitude of the ratio of the total charges
stored by the capacitors in circuit A to
circuit B is
A. 9.
B. 3.
C. 1/3.
D. 1/9.
0.25 F
HKAL Extra Exercise Chapter 14 Capacitance
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14.
16.
C1
B
A
C2
1 F
A
S
C3
2 F
15.
70 V
4 F
4 F
Output
12 F
0V
0V
Three capacitors are connected to a 70 V
supply as shown in the above circuit. The
voltage at the output is
A. 10 V.
B. 28 V.
C. 42 V.
D. 60 V.
4 F
D
A voltage of 1000 V is applied across AB
in the capacitor network shown above.
The voltage across CD is found to be 450
V. If after some time, the voltage across
CD suddenly jumps to 0 V, which
capacitor(s) has been shorted ?
A. 1μF
B. 2μF
C. 4μF
D.
All 4 capacitors have been shorted.
17.
C1
C2
A charged capacitor C1 is connected to an
uncharged capacitor C2 as shown. If
E1 = the total energy stored in C1 and C2
before connection, and
E2 = the total energy stored in C1 and C2
after connection,
Which of the following is/are correct?
(1) The charges discharged by C1 is
equal to the charges charged in C2.
(2) After connection, the charges stored
in C1 is equal to that in C2.
(3) After connection, the p.d. across C1
and C2 are in the ratio
capaci tan ce of C1
capaci tan ce of C 2
A.
C.
D.
HKAL Extra Exercise Chapter 14 Capacitance
C
B
In the above circuit, two charged
capacitors C1 and C2 are connected across
AB so that it is parallel with an initially
uncharged capacitor C3. Which of the
following statements is/are correct when
switch S is closed ?
(1) The quantity of charge on C1 is the
same as that on C3.
(2) The combined capacitance across AB
will increase.
(3) The potential difference across AB
will increase.
A. (2) only
B. (3) only
C. (1) and (2) only
E. (1), (2) and (3)
3 F
(1) only
B.
(1) and (2) only
(2) and (3) only
.
(3) only
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14.3 Energy Stored in a Capacitor
18. The energy of a 9μF capacitor when having a stored charge Q is E. The energy of a 3μF
when having a stored charge 2 Q is
A. 4/3 E.
B. 2 E.
C.
4 E.
D.
12 E.
19. The two plates of a parallel-plate capacitor initially carry equal amounts of positive charge. If
some charges are transferred from one plate to another, the charges on the plates are
respectively -300μC and -700μC. The potential difference across the plates becomes 80 V.
What is the capacitance of the capacitor ?
A. 2.5μF
B. 3.8μF
C.
8.8μF
D.
12.5μF
Charging a Capacitor with a Cell
In the above circuit, the battery has an
20.
e.m.f. of 9.0 V and all the capacitors are
identical. Initially none of the capacitors
are charged. The switch is first connected
to X and then to Y. What is the final
potential difference between Z and Y ?
A. 1.0 V
B. 1.5 V
C. 3.0 V
D. 9.0 V
A.
A parallel-plate capacitor is connected to a
battery as shown. What will happen if the
separation of the plates is decreased?
capacitance voltage
charge
increases
decreases
increases
B.
C.
D.
increases
decreases
increases
unchanged
decreases
unchanged
increases
increases
decreases
21.
X
Y
9.0 V
Moving Apart Two Charged Plates
22. A parallel-plate capacitor is charged by a
battery and the energy stored in the
capacitor is E. The circuit is still
connected to the battery. If one of the
plates
is
moved
so
that
the
plate-separation is halved, the electrical
energy stored in the capacitor will
A. decrease to E/4.
B remain the same.
C increase to 2E.
D
increase to 4E.
Z
23. A parallel-plate capacitor is charged by a constant voltage source. With the plates disconnected
from the source, the plate separation, d, is then gradually increased from an initial value d0.
Which of the following graphs best shows the relationship between the energy, U, stored in the
capacitor and plate separation, d ?
HKAL Extra Exercise Chapter 14 Capacitance
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A.
B.
U
C.
U
0
d0
U
0
d0
d
D.
d
U
0
d0
d
0
d0
d
14.4 Charging and Discharging
24. A capacitor has a capacitance of 1 farad. Which of the following deductions must be correct ?
(1) It gains 1 joule of electrical energy when it has 1 coulomb of charge.
(2) It stores 1 coulomb of charge at a potential difference of 1 volt.
(3) It will be fully discharged in 1 second by a constant current of 1 ampere.
A.
(1) only
B.
(2) only
C.
(1) and (2) only
D.
(2) and (3) only
Charging a Capacitor At a Constant Rate
25. A capacitor is charged by a constant current. Which of the following graphs shows the time
variation of the charge stored in the capacitor during the charging process ?
A.
B.
C.
D.
charge
charge
time
charge
time
charge
time
time
Charging a capacitor via a resistor
26.
R
C
K
d.c.
A capacitor and a resistor are connected in series to a d.c. voltage supply as shown. At time t =
0, the key K is closed. Which of the following statements is/are true?
(1) The final charge on the capacitor does not depend on the resistance of R in the circuit.
(2) The capacitor is almost fully charged after a time t = CR.
(3) At any time t the potential differences across R is a constant.
A. (1) only
B. (3) only
C. (1) and (2) only
D. (2) and (3) only
HKAL Extra Exercise Chapter 14 Capacitance
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27.
28.
E
C
A
V
VR
R
B
VAC
0
D
C
t
R
A changing voltage V is applied across AB
in the circuit shown. The potential
difference VAC across the capacitor is
found to vary with time t as shown. Which
of the following graphs shows the
variation of potential difference VR across
An initially uncharged capacitor of
capacitance C is connected in series with a
resistor R and a battery of e.m.f. E. What
will be (1) the energy dissipated by R in
fully charging up C and (2) the total work
done by the battery in fully charging up
the resistor R with time t ?
A.
B.
C?
VR
0
Work done by Energy stored
battery
in C
2
1 CE
A.
0
2
VR
t
C.
0
t
D.
VR
0
B.
C.
D.
CE2
1 C E2
2
CE2
0
C E2
1 C E2
2
VR
t
0
t
Time constant
29. A 4μF capacitor is discharged through a resistor R. If the time constant of the discharging
circuit is 5 ms, what is the resistance of the resistor ?
A. 20 kΩ
B. 2 kΩ
C.
1.3 kΩ
D.
0.8 kΩ
Discharging a capacitor via a resistor
30. A capacitor is charged to a p.d. of 150 V and then connected across a resistor. After 1 s, the p.d.
across the capacitor is 100 V. The time constant of the circuit is
A. 0.22 s.
B. 0.41 s.
C. 2.47 s.
D. 5 s.
31.
C
R
A
HKAL Extra Exercise Chapter 14 Capacitance
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A charged capacitor C, of 15μF capacitance, is connected in the circuit above. For a period of
20 s, the current is kept constant at 30μA by continuous adjustment of R. During this period,
the p.d. across the capacitor has fallen by
A. 40 V.
B. 7 V.
C.
2 V.
D.
0.6 mV.
32. A 4μF capacitor, which is initially charged, is discharged through a 25 Ω resistor. The initial
charge on the capacitor is 4 × 10-3 C. What is the maximum current during discharge ?
A.
400 A
B.
100 A
C.
40 A
D.
0.1 A
33. A charged capacitor is connected across a resistor. Its voltage drops to one-fifth of the original
value in 20 s. Find the time constant of the circuit.
A. 100 s
B. 32.2 s
C. 15.0 s
D. 12.4 s
34. A charged capacitor is connected to a voltmeter with resistance 1 MΩ. The voltmeter reading
drops from 8 V to 6 V in 11.2 s. Find the of capacitance of the capacitor.
A. 39μF.
B. 20μF.
C. 6.3μF.
D.
5.4μF.
35.
i / mA
50
25
0
5
10
15
20
t/s
A capacitor C is charged to a certain p.d. and then discharged through a resistor R. The
variation of the current i with time t is shown in the above graph. Which of the following is/are
correct ?
(1) The time constant of the circuit is about 3.6 s.
(2) The area under the graph is proportional to the square root of the charge stored in the
capacitor.
(3) If the resistance of R is halved, the current at t = 0 will also be halved.
A. (1) only
B. (3) only
C. (1) and (2) only
D. (2) and (3) only
36. A ‘jumbo’ capacitor has capacitance 500 000μF. Such a capacitor charged to 25 V would
(1) provide a mean current of 1 mA for 12500 s.
(2) be completely discharged through a 0.2 Ω resistor in 1 s.
(3) store 156 J of electrostatic energy.
A. (1) only
B. (3) only
HKAL Extra Exercise Chapter 14 Capacitance
C.
(1) and (2) only
D.
(2) and (3) only
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37.
40.
100 k 50 V
8 F
S
S
P
C
E
To
CRO
R
Q
8 M
In the circuit shown, S is connected to P
until the capacitor is fully charged. Then S
is switched to Q. What is the initial value
of the current through the 8 M Ω
In the above circuit, a capacitor C is
charged from a battery E and then
completely discharged through a resistor R
using a vibrating reed switch S. The
resistor ?
A. 1.6 × 10-6 A B. 3.0 × 10-6 A
C. 6.3 × 10-6 A
D. 4.0 × 10-4 A
waveform displayed on the screen of the
CRO with suitable time base should be
A.
B.
38. In a circuit with a vibrating reed switch, a
7μF capacitor is charged from a battery
of e.m.f. 5 V and completely discharged
through a resistor with a frequency of 20
Hz. The average power dissipated as heat
in the resistor is
A. 25μW.
B. 35μW.
C. 600μW.
D. 1.8 mW.
39.
C.
D.
41.
VS
S
B
R
C
0 1
2 3
1 mF
t / ms
VS
4
V
Using the vibrating reed switch S, in the
above circuit, the capacitor C is charged
from battery B and completely discharged
through the resistor R with a frequency of
(a)
(b)
A square wave voltage VS, as shown in
Figure (a), is applied to a circuit
containing a 1 mF capacitor and a 4 Ω
30 Hz. When a CRO is connected across C,
the wave form will look like :
A.
B.
resistor connected in series. Which of the
following graphs best represents the
variation of the p.d. V across the resistor
with time t ?
C.
D.
HKAL Extra Exercise Chapter 14 Capacitance
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A.
B.
V
V
0
C.
0
1
2 t / ms
D.
V
1
2 t / ms
0
V
1
2 t / ms
0
1
2 t / ms
42.
C1
S
R
C2
A charged capacitor C1 , is connected to an uncharged capacitor C2 of smallr capacitance
through a resistor R as shown above. When switch S is closed, which of the following
statements is correct ?
A. The total charges on the two capacitors falls.
B. The final charge on C2 is greater than that on C1 .
C. The total energy stored in the capacitors falls.
D. The potential difference across C1 falls.
KEY :
1 – 10 : BDDBC, DADAB, 11 – 20 : CADAB, DADAB,
21 – 30 : BCABD, ADCCC, 31 – 40 : ACDAA, CCDCB,
41 – 42 : CB.
HKAL Extra Exercise Chapter 14 Capacitance
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