Capacitor Assignment

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CAPACITOR ASSIGNMENT
Section A : Objective Type Questions
1. A graph between current and time during charging of a capacitor by a battery in series with
a resistor is shown. The graphs are drawn for two circuits. 𝑅1 , 𝑅2 , 𝐶1 , 𝐶2 and 𝑉1 , 𝑉2 are the
values of resistance, capacitance and EMF of the cell in the two circuits. If only two
parameters (out of resistance, capacitance, EMF) are different in the two circuits. What may
be the correct option(s)?
(a) 𝑉1 = 𝑉2 , 𝑅1 > 𝑅2 , 𝐶1 > 𝐶2 (b) 𝑉1 > 𝑉2 , 𝑅1 > 𝑅2 , 𝐶1 = 𝐶2

(c) 𝑉1 < 𝑉2 , 𝑅1 < 𝑅2 , 𝐶1 = 𝐶2 (d) 𝑉1 < 𝑉2 , 𝑅1 = 𝑅2 , 𝐶1 < 𝐶2
2. A capacitor of capacitance C is charged by a battery of emf E and internal resistance r. A

resistance 2r is also connected in series with the capacitor. The amount of heat liberated
inside the battery by the time capacitor is 50% charged is
𝐸2 𝐶 𝐸2 𝐶 𝐸2 𝐶 𝐸2 𝐶
(a) (b) (c) (d)
8 6 12 24
3. A fully charged capacitor has a capacitance C. It is discharged through a small coil of

resistance wire embedded in a thermally insulated block of specific heat capacity s and mass
m. If the temperature of the block is raised by ∆T, the potential difference V across the
capacitance is
2𝑚𝐶∆𝑇 𝑚𝐶∆𝑇 𝑚𝑠∆𝑇 2𝑚𝑠∆𝑇

(a) √ 𝑠
(b) 𝑠
(c) 𝐶
(d) √ 𝐶
4. A capacitor of capacity C is charged to a potential difference V and another capacitor of
capacity 2C is charged to a potential difference 4 V. The charging batteries are disconnected
and the two capacitors are connected with reverse polarity (i.e. positive plate of first capacitor
is connected to negative plate of second capacitor). The heat produced during the
redistribution of charge between the capacitors will be
125 𝐶𝑉 2 50 𝐶𝑉 2 25 𝐶𝑉 2
(a) (b) (c) 2 C𝑉 2 (d)
3 3 3
5. Consider the arrangement of three plates X, Y and Z each of the area A and separation d.
The energy stored when the plates are fully charged is
(a) 𝜀0 𝐴𝑉 2 /2d (b) 𝜀0 𝐴𝑉 2 /d (c) 2𝜀0 𝐴𝑉 2 /d (d) 3𝜀0 𝐴𝑉 2 /d
6. Consider a capacitor - charging circuit. Let 𝑄1 be the charge given to the capacitor in time
interval of 20 ms and 𝑄2 be the charge given in the next time interval of 20 ms. Let 10𝜇C
charge be deposited in a time interval 𝑡1 and the next 10𝜇C charge is deposited in the next
time interval 𝑡2 . Then,
(a) 𝑄1 > 𝑄2 , 𝑡1 > 𝑡2 (b) 𝑄1 > 𝑄2 , 𝑡1 < 𝑡2
(c) 𝑄1 < 𝑄2 , 𝑡1 > 𝑡2 (d) 𝑄1 < 𝑄2 , 𝑡1 < 𝑡2
7. A 2𝜇F capacitor is charged as shown in the figure. The percentage of its stored energy
dissipated after the switch S is turned to position 2 is
(a) 0% (b) 20% (c) 75% (d) 80%
8. Four capacitors are connected as shown in the figure to a 30 V battery. The potential
difference between points a and b is
(a) 5 V (b) 9 V (c) 10 V (d) 13 V

9. Three uncharged capacitors of capacitance 𝐶1 , 𝐶2 and 𝐶3 are connected to one another as
shown in figure. The potential at O will be
49 3
(a) 3 V (b) 11 𝑉 (c) 4 V (d) 11 𝑉
10. The potential difference between points a and b of circuits shown in the figure is
𝐸1 + 𝐸2 𝐸1 − 𝐸2 𝐸1 + 𝐸2 𝐸1 − 𝐸2
(a) ( ) 𝐶2 (b) ( ) 𝐶2 (c) ( ) 𝐶1 (d) ( ) 𝐶1
𝐶1 + 𝐶2 𝐶1 + 𝐶2 𝐶1 + 𝐶2 𝐶1 + 𝐶2
11. A capacitor 𝐶1 is charged to a potential V and connected to another capacitor in series

with a resistor R as shown. It is observed that head 𝐻1 is dissipated across resistance R, till
the circuit reaches steady state. Same process is repeated using resistance of 2R. If 𝐻2 is heat
dissipated in this case, then
𝐻 𝐻 𝐻 1 𝐻
(a) 𝐻2 = 1 (b) 𝐻2 = 4 (c) 𝐻2 = (d) 𝐻2 = 2
1 1 1 4 1
12. A leaky parallel capacitor is filled completely with a material having dielectric constant
K = 5 and electrical conductivity 𝜎 = 7.4 x 10−12 Ω−1 𝑚−1 . Charge on the plate at instant t = 0
is q = 8.885μC. Then, time constant of leaky capacitor is
(a) 3 s (b) 4 s (c) 5 s (d) 6 s
13. Five identical capacitor plates are arranged such that they make four capacitors each of
2μF. The plates are connected to a source of emf 10V. The charge on plate C is
(a) +20μC (b) +40μC (c) +60μC (d) +80μC
14. The capacities and connection of five capacitors are shown in the figure. The potential
difference between the points A and B is 60 V. Then, the equivalent capacity between A and
B and the charge on 5 μF capacitance will be respectively
(a) 44 μF , 300 μC (b) 16 μF , 150 μC (c) 15 μF , 200 μC (d) 4 μF , 50 μC
15. Two capacitors A and B with capacities 3μF and 2µf are charged to a potential difference
of 100 V and 180 V respectively. The plates of the capacitors are connected as shown in the
figure with one wire of each capacitor free. The upper plate of A is positive and that of B is
negative. An uncharged 2μF capacitor C with lead wires falls on the free ends to complete the
circuit, then charges on the three capacitors are
(a) 𝑞1 = 90 μC, 𝑞2 = 150 μC and 𝑞3 = 210 μC

(b) 𝑞1 = 210 μC, 𝑞2 = 90 μC and 𝑞3 = 150 μC
(c) 𝑞1 = 90 μC, 𝑞2 = 210 μC and 𝑞3 = 150 μC
(d) 𝑞1 = 150 μC, 𝑞2 = 90 μC and 𝑞3 = 210 μC
Note Here 𝑞1 is the charge on A and 𝑞3 the charge on B.
16. A parallel plate capacitor with dielectric of dielectric constant K between the plates has a
capacity C and is charged to a potential of V volt and battery remains connected. The
dielectric slab is slowly removed from the plates and then reinserted. The net work done by
the system in the process is
1
(a) 2 (𝑘 − 1)𝐶𝑉 2 (b) 𝐶𝑉 2 (k-1)K (c) (𝑘 − 1)𝐶𝑉 2 (d) zero
17. In the given circuit, a charge of +80𝜇C is given to the upper plate of the 4𝜇F capacitor.
Then in the steady state, the charge on the upper plate of the 3𝜇F capacitor is
(a) +32 𝜇C (b) +40 𝜇C (c) +48 𝜇C (d) +80 𝜇C
18. For the circuit shown, which of the following statements is true?
(a) With 𝑆1 closed, 𝑉1 = 15V, 𝑉2 = 20V
(b) With 𝑆3 closed, 𝑉1 = 𝑉2 = 25V
(c) With 𝑆1 and 𝑆1 closed, 𝑉1 = 𝑉2 = 0
(d) With 𝑆3 closed, 𝑉1 = 30V, 𝑉2 = 20V
19. A parallel plate capacitor C with plates of area 1 square unit and separation d is filled
with a liquid of dielectric constant K = 2. The level of liquid is d/3, initially. If the liquid
level decreases at a constant speed v. Then, the capacity of capacitor after t second is
6𝜀0 (15𝑑 + 9𝑣𝑡)𝜀0
(a) (b)
5𝑑 + 3𝑣𝑡 2𝑑2 − 3𝑑𝑣𝑡 − 9𝑣 2 𝑡 2
6𝜀0 (15𝑑 + 9𝑣𝑡)𝜀0

(c) (d)
5𝑑 − 3𝑣𝑡 2𝑑2 + 3𝑑𝑣𝑡 − 9𝑣 2 𝑡 2
Note : More than one correct options in Q - 20
20. In the given circuit, the relationship between voltage of point A, B and C are
(a) 𝑉𝐴𝐵 = 25V (b) 𝑉𝐴𝐵 = 27V (c) 𝑉𝐵𝐶 = 75V (d) 𝑉𝐵𝐶 = 50V
Section B : Subjective Type Questions

21. A capacitor of capacitance 5µF is connected to a source of constant emf of 200 V. Then,
the switch was shifted to contact 2 from contact 1. Find the amount of heat generated in the
400 Ω resistance.
22. Analyze the given circuit in the steady state condition. Charge on the capacitor is
𝑞0 = 16μC.
(a) Find the current in each branch
(b) Find the emf of the battery.
(c) If now the battery is removed and the points A and C are shorted. Find the time during
which charge on the capacitor becomes 8μC.
23. In the given circuit diagram, find the charges which flow through directions 1 and 2 when
switch S is closed.
24. Initially, the switch is in position 1 for a long time. At t = 0, the switch is moved from 1
to 2. Obtain expression for 𝑉𝑐 and 𝑉𝑅 for t > 0.
25. In the shown network, find the charge on capacitors of capacitances 5 𝜇F and 3 𝜇F, in
steady state.

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SHEORAN CLASSES

An Institution for I.I.T-JEE & Medical

(a) 𝑉1 = 𝑉2 , 𝑅1 > 𝑅2 , 𝐶1 > 𝐶2 (b) 𝑉1 > 𝑉2 , 𝑅1 > 𝑅2 , 𝐶1 = 𝐶2

2. A capacitor of capacitance C is charged by a battery of emf E and internal resistance r. A

3. A fully charged capacitor has a capacitance C. It is discharged through a small coil of

2𝑚𝐶∆𝑇 𝑚𝐶∆𝑇 𝑚𝑠∆𝑇 2𝑚𝑠∆𝑇

(a) 𝜀0 𝐴𝑉 2 /2d (b) 𝜀0 𝐴𝑉 2 /d (c) 2𝜀0 𝐴𝑉 2 /d (d) 3𝜀0 𝐴𝑉 2 /d

(a) 0% (b) 20% (c) 75% (d) 80%

(a) 5 V (b) 9 V (c) 10 V (d) 13 V

11. A capacitor 𝐶1 is charged to a potential V and connected to another capacitor in series

(a) 3 s (b) 4 s (c) 5 s (d) 6 s

(a) 44 μF , 300 μC (b) 16 μF , 150 μC (c) 15 μF , 200 μC (d) 4 μF , 50 μC

(a) 𝑞1 = 90 μC, 𝑞2 = 150 μC and 𝑞3 = 210 μC

(a) +32 𝜇C (b) +40 𝜇C (c) +48 𝜇C (d) +80 𝜇C

6𝜀0 (15𝑑 + 9𝑣𝑡)𝜀0

Section B : Subjective Type Questions

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