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### Transcript of Course: Capacitors

Course: Capacitors
Presented by Kailash Sharma
Use referral code KAILASH10 to get 10% discount on subscriptions on
KAILASH SHARMA (REF-KAILASH10) 2 | P a g e
EXERCISE-I Part-I
(Capacitance and Types of capacitors)
1. The radii of two metallic spheres are 5 cm and 10 cm and both carry equal
charge of 75μC. If the two spheres are shorted then charge will be transferred–
(A) 25 μC from smaller to bigger (B) 25 μC from bigger to smaller (C) 50 μC from smaller to bigger (D) 50 μC from bigger to smaller
2. Two isolated charged metallic spheres of radii R1 and R2 having charges Q1 and Q2 respectively are connected to each other, then there is:
(A) No change in the electrical energy of the system (B) An increase in the electrical energy of the system (C) A decrease in the electrical energy of the system in any case
(D) A decrease in electrical energy of the system if 1 2 2 1Q R Q R
3. A parallel plate capacitor is charged and then isolated. On increasing the plate separation– Charge Potential Capacitance
(A) remains constant remains constant decreases (B) remains constant increases decreases (C) remains constant decreases increases (D) increases increases decreases
4. The plates of a parallel plate condenser are being moved away with a constant speed v. If the plate separation at any instant of time is d then the rate of change of capacitance with time is proportional to–
(A) 1
d (B)
d (C) d2 (D) d
5. The capacitance (C) for an isolated conducting sphere of radius (a) is given by 4πε0a. If the sphere is enclosed with an earthed concentric sphere. The ratio of
the radii of the spheres being n
(n-1) then the capacitance of such a sphere will
be increased by a factor
(A) n (B) −
KAILASH SHARMA (REF-KAILASH10) 3 | P a g e
6. Plate A of a parallel air filled capacitor is connected to a spring having force
constant k and plate B is fixed. If a charge +q is placed on plate A and charge
–q on plate B then find out extension in spring in equilibrium. Assume area of plate is ‘A’
(A)
2
0
Q
2k A (D) None of these
7. Three long concentric conducting cylindrical shells have radii R, 2R and 2 2 R.
Inner and outer shells are connected to each other. The capacitance across middle and inner shells per unit length is
(A)
0
1
2 n2l (D) None of these
8. Two spherical conductors A1 and A2 of radii r1 and r2 are placed concentrically in air. The two are connected by a copper wire as shown in figure. Then the equivalent capacitance of the system is
(A) −
4π kr .r
r r (B) ( )0 1 24π r +r (C) 0 24π r (D) 0 14π r
9. There are two conducting spheres of radius a and b (b > a) carrying equal and opposite charges. They are placed at a separation d (>>> a and b). The capacitance of system is
(A) − −
04πε
KAILASH SHARMA (REF-KAILASH10) 4 | P a g e
10. A Conducting body 1 has some initial charge Q, and its capacitance is C. There
are two other conducting bodies 2 and 3, having capacitances: C2 = 2C and
C3 → . Bodies 2 and 3 are initially uncharged. “Body 2 is touched with body 1. Then, body 2 is removed from body 1 and touched with body 3, and then removed.” This process is repeated N times. Then the charge on body 1 at the end must be
(A) Q/3N (B) Q/3N–1 (C) Q/N3 (D) None of these
11. You have a parallel plate capacitor, a spherical capacitor and a cylindrical capacitor. Each capacitor is charged by and then removed from the same
battery. Consider the following situations (i) the separation between the plates of the parallel plate capacitor is reduced (ii) the radius of the outer spherical shell of the spherical capacitor is increased (iii) the radius of the outer cylinder of the cylindrical capacitor is increased Which of the following is correct?
(A) In each of these situations (i), (ii) and (iii), charge on the given capacitor remains the same and potential difference across it also remains the same
(B) In each of these situations (i), (ii) and (iii), charge on the given capacitor remains the same but potential difference, in situations (i) and (iii),
decreases, and in situation (ii), increases
(C) In each of these situations (i), (ii) and (iii), charge on the given capacitor remains the same but potential difference, in situations (i), decreases, and in situations (ii) and (iii), increases
(D) Charge on the capacitor in each situation changes. It increases in all these situations but potential difference remains the same
12. The work done against electric forces in increasing the potential difference of a
condenser from 20V to 40V is W. The work done in increasing its potential difference from 40V to 50V will be (consider capacitance of capacitor remain constant)
(A) 4W (B) 3W
4 (C) 2W (D)
W
2
13. A capacitor of capacitance C is initially charged to a potential difference of V volt. Now it is connected to a battery of 2V with opposite polarity. The ratio of
heat generated to the final energy stored in the capacitor will be
(A) 1.75 (B) 2.25 (C) 2.5 (D) 1/2
KAILASH SHARMA (REF-KAILASH10) 5 | P a g e
Paragraph for Qus 14 to 17
A parallel plate capacitor is charged up to a potential of 300 volts. Area of the
plates is 100 cm2 and spacing between them is 2 cm. If the plates are moved
apart to a distance of 2.5 cm without disconnecting the power source, then
( -12 2 -1 -2 0= 9×10 C N m ):
14. Electric field inside the capacitor when distance is 2.5 cm :
(A) 15 × 102 V/m (B) 3 × 103 V/m (C) 12 × 103 V/m (D) 6 × 103 V/m
15. Change in energy of the capacitor is :
(A) 6 × 10–8 J (B) – 1215 × 10–10 J
(C) 1215 × 10–10 J (D) – 405 × 10–10 J
16. If the distance is increased after disconnecting the power source, then electric field inside the capacitor is
(A) 6 × 103 V/m (B) 3 × 103 V/m (C) 12 × 103 V/m (D) 15 × 103 V/m
17. Change in energy of the capacitor in above case is :
(A) 303.75 × 10–9 J (B) – 1215 × 10–10 J (C) 5.06 × 10–8 J (D) – 303.75 × 10–9 J
18. Each plate of a parallel plate air capacitor has an area S. what amount of work has to be performed to slowly increase the distance between the plates from x1 to x2 if : (i) the charge of the capacitor, which is equal to q or
(A)
2 S
(ii) the voltage across the capacitor, which is equal to V, is kept constant in the process.
(A)
KAILASH SHARMA (REF-KAILASH10) 6 | P a g e
19. Three large plates are arranged as shown. How much charge will flow through
the key k if it is closed?
(A) 5Q
6 (B)
Section-B (Combination of Capacitors)
20. A 3μF capacitor is charged up to 300 volt and 2μF is charged up to 200 volt. The capacitors are connected so that the plates of same polarity are connected
together. The final potential difference between the plates of the capacitor after they are connected is :
(A) 220 V (B) 160 V (C) 280 V (D) 260 V
21. In the circuit shown in figure charge stored in the capacitor of capacity 5μf is
(A) 60 μ C (B) 20 μ C (C) 30 μ C (D) zero
22. Three uncharged capacitors of capacitance C1= 1μF, C2 =2μF and C3 = 3μF are connected as shown in figure to another and to point A, B and D potential A = 10V, B = 25V and D = 20V, Determine the potential (0) at point O.
(A) 20 V (B) 30 V (C) 40 V (D) 10 V
KAILASH SHARMA (REF-KAILASH10) 7 | P a g e
23. Five capacitors are connected as shown in the figure. Initially S is opened and
all capacitors are uncharged. When S is closed, steady state is obtained. Then
find out potential difference between the points M and N.
(A) 14 (B) 12 (C) 10 (D) 15
24. If charge on left plane of the 5μ F capacitor in the circuit segment shown in the figure is 20μ C, the charge on the right plate of 3μ F capacitor is
(A) +8.57 μ C (B) –8.57 μ C (C) +11.42 μ C (D) –11.42 μ C
25. What is the equivalent capacitance of the system of capacitors between A & B
(A) 7
C 6
26. Find the equivalent capacitance across A & B
(A) 28
μF 3
(B) 15
μF 2
KAILASH SHARMA (REF-KAILASH10) 8 | P a g e
27. Two capacitor having capacitances 8μF and 16μF have breaking voltages 20V
and 80V. They are combined in series. The maximum charge they store
individually in the combination is
(A) 160 μ C (B) 200 μ C (C) 1280 μ C (D) none of these
28. The diagram shows four capacitors with capacitances and break down voltages as mentioned. What should be the maximum value of the external emf source such that no capacitor breaks down? [Hint: first of all find out the break down voltages of each branch. After that compare them.]
(A) 2.5 KV (B) 10/3 KV (C) 3 KV (D) 1 KV
29. In the circuit shown, the energy stored in 1μF capacitor is
(A) 40μ J (B) 64 μ J (C) 32μ J (D) None
30. Find equivalent capacitance across AB (all capacitance in μF)
(A) 20
μF 3
KAILASH SHARMA (REF-KAILASH10) 9 | P a g e
31. A 10μF capacitor and a 20μF capacitor are connected in series across a 200 V
supply line. The charged capacitors are then disconnected from the line and
reconnected such that those same polarities are connected to each other and no external voltage is applied. The potential difference across capacitors is
(A) 400
V 9
(B) 800
V 3
(C) 400V (D) 200 V
32. The equivalent capacitance between A and B, where concentric spherical shells having radius a and b are connected as shown in the figure.
(A) −
(b a) (D) none of these
33. In the given figure the work done by the battery after the switch S is closed is
(A) 100 μJ (B) – 100 μJ (C) 80 μJ (D) – 80 μJ
KAILASH SHARMA (REF-KAILASH10) 10 | P a g e
34. The potential at point A, in the circuit, is (Point N is grounded, i.e, the potential
of that point is zero.)
(A) 10 V (B) 7.5 V (C) 5 V (D) 2.5 V
35. Three parallel plate air capacitors are connected in parallel. Each capacitor has plate area A/3 and the separation between the plates is d, 2d and 3d
respectively. The equivalent capacity of combination is (e0 = absolute permittivity of free space)
(A) 07ε A
18d
36. A, B, C, D, E, F are conducting plates each of area A and any two consecutive
plates separated by a distance d. The net energy stored in the system after the switch is closed is
(A) 203ε A
V d
37. Four identical capacitors are connected with a battery of voltage V and two switches k1 and k2 as shown in the figure below. Initially, k1 is closed, now if k2
is also closed, find the heat loss.
(A) 21
CV 2
(B) 22
CV 3
(C) 21
CV 3
(D) 21
CV 4
KAILASH SHARMA (REF-KAILASH10) 11 | P a g e
38. Four metal plates are arranged as shown in the figure. Capacitance between X
and Y (A → Area of each plate, d → distance between the plates) is
(A) 0ε A3
d (C) 0ε A2
d
39. Five conducting parallel plates having area A and separation between then d, are placed as shown in the figure. Plate number 2 and 4 are connected wire and between point A and B, a ell of emf E is connected. The charge flown through the cell is
(A) 0ε AE3
d (D) 0ε AE
2d
40. Three plates A, B and C each of area 0.1 m2 are separated by 0.885mm from each other as shown in the figure. A 10 V battery is used to charge the system. The energy stored in the system is
(A) 1μ J (B) 10–1 μ J (C) 10–2 μ J (D) 10–3 μ J
KAILASH SHARMA (REF-KAILASH10) 12 | P a g e
41. Four metallic plates are arranged as shown in the figure. If the distance
between each plate then capacitance of the given system between points A and
B is (Given d < < A)
(A) 0ε A
d
42. A 2μF capacitor is charged to a potential = 10 V. Another 4μF capacitor is charged to a potential = 20V. The two capacitors are then connected in a single
loop, with the positive plate of one connected with negative plate of the other. What heat is evolved in the circuit ?
(A) 300μ J (B) 600μ J (C) 900μ J (D) 450μJ
Section-C (Circuits with Resistors and Capacitors)
43. The magnitude of charge in steady state on either of the plates of condenser C in the adjoining circuit is-
(A) CE (B) 2
(R +r)
44. In steady state, find the charge on the capacitor shown in figure.
(A) 4 μC (B) 5 μC (C) 6 μC (D) 7 μC
KAILASH SHARMA (REF-KAILASH10) 13 | P a g e
45. In the circuit shown in figure the capacitors are initially uncharged. The
current through resistor PQ just after closing the switch is :
(A) 2A from P to Q (B) 2A from Q to P (C) 6A from P to Q (D) zero
46. In the circuit shown, the cell is ideal, with emf = 15 V. Each resistance is of 3Ω. The potential difference across the capacitor is
(A) zero (B) 9 V (C) 12 V (D) 15 V
47. Find heat produced in the capacitors on closing the switch S
(A) 0.0002 J (B) 0.0005 J (C) 0.00075 J (D) zero
KAILASH SHARMA (REF-KAILASH10) 14 | P a g e
Section-D (Charging and discharging of capacitors)
48. The time constant of the circuit shown is :
(A) RC
2 (B)
RC
4
49. A capacitor of capacitance 100 μF is connected across a battery of emf 6.0 V through a resistance of 20 kΩ for 4.0s. The battery is then replaced by a thick wire. Want will be the charge on the capacitor 4.0 s after the battery is disconnected?
(A) 70 μ (B) 80 μ (C) 60 μ (D) none of these
50. A capacitor C =100 μ F is connected to three resistor each of resistance 1kΩ and a battery of emf 9V. The switch S has been closed for long time so as to charge the capacitor. When switch S is opened, the capacitor. Discharges with
time constant
(A) 33ms (B) 5 ms (C) 3.3 ms (D) 50 ms
51. In the transient shown the time constant of the circuit is :
(A) 5
RC 3
(B) 5
RC 2
(C) 7
RC 4
(D) 7
RC 3
KAILASH SHARMA (REF-KAILASH10) 15 | P a g e
52. In the circuit shown, when the key k is pressed at time t = 0, which of the
following statements about current I in the resistor AB is true
(A) I = 2mA at all t (B) I oscillates between 1 mA and 2 mA
(C) I = I mA at all t (D) At t = 0, I = 2mA and with time it goes to 1 mA
53. A 5.0 μF capacitor having a charge of 20 μC is discharged through a wire of resistance of 5.0 Ω. Find the heat dissipated in the wire between 25 to 50 μs after the capacitors are made.
(A) 4.7 μJ (B) 3.7 μJ (C) 5.7 μJ (D) 2.7 μJ
54. In the circuit shown in figure C1 = 2C2. Switch S is closed at time t = 0. Let i1
and i2 ne the currents flowing through C1 and C2 at any time t, then the ratio i1/i2
(A) is constant (B) increases with increase in time t (C) decreases with increase in time t (D) first increases then decreases
55. A charged capacitor is allowed to discharge through a resistance 2Ω by closing the switch S at the instant t = 0. At time t = ln2μs, the reading of ammeter falls
half of its initial value. The resistance of the ammeter equal to
(A) 0 (B) 2Ω (C) ∞ (D) 2MΩ
KAILASH SHARMA (REF-KAILASH10) 16 | P a g e
56. The capacitor shown in the figure is initially uncharged, the battery is ideal.
The switch S is closed at time t = 0, then the time after which the energy stored
in the capacitor becomes one fourth of the energy stored it in steady-state is:
(A) RC (B) RC ln 2 (C) RC ln 4 (D) 2RC
Section-E (Capacitors with dielectric)
57. The distance between plates of a parallel plate capacitor is 5d. Let the positively charged plate is at x = 0 and negatively charged plate is at x = 5d. Two slabs
one of conductor and other of a dielectric of equal thickness d are inserted
between the plates as shown in figure. Potential versus distance graph will look like:
(A) (B) (C) (D)
KAILASH SHARMA (REF-KAILASH10) 17 | P a g e
58. A parallel plate capacitor has layers of dielectric as shown in figure. This
capacitor is connected across a battery. The graph which shows the variation of
electric field (E) and distance (x) from left plate.
(A) (B)
(C) (D)
59. Hard rubber has a dielectric constant of 2.8 and a dielectric strength of 18 ×108 volts/meter if it is used as the dielectric material filling the full space in a parallel plate capacitor. What minimum area may the plates of the capacitor have in order that the capacitor be 7.0 × 10–2 μf and that the capacitor be able
to withstand a potential difference of 4000 volts.
(A) 0.62 m–2 (B) 0.32 m–2 (C) 0.42 m–2 (D) 0.52 m–2
60. Two parallel plate air capacitors each of capacitance C were connected in series to a battery with e.m.f ε. Then one of the capacitors was filled up with uniform dielectric with relative permittivity k. What amount of charge flows through the battery?
(A) −
2 k 1 (B)
2 k +1 (C)
KAILASH SHARMA (REF-KAILASH10) 18 | P a g e
61. A parallel-plate of a capacitor of plate area A and plate separation d is charged
to a potential difference V and then the battery is disconnected. A slab of
dielectric constant K is then inserted between the plates of the capacitor so as to fill the whole space between the plates. Find the work done on the system in the process of inserting the slab.
(A)
+1 d K
62. An air-filled parallel plate capacitor has capacitance C. The capacitor is
connected through a resistor to a voltage source providing a constant potential difference V.
A dielectric plate with a dielectric constant K is inserted into the capacitor,
filling it completely. After the equilibrium is established plate is quickly removed. Find the amount of heat generated in the resistor by the time, the equilibrium is re-established.
(A) CV2 (K – 1) (B) −21 CV (K 1)
2 (C) CV2 (K – 1)2 (D)
2 −21 CV (K 1)
2
63. A parallel plate capacitor of area A, plate separation d and capacitance C is filled with three dielectric materials having dielectric material constants k1, k2, and k3 as shown. If a single dielectric material is to be used to have the same
capacitance C in the capacitor, then its dielectric constant k is given by
(A) k = k1 + k2 + 2k3 (B) 1 2 3
1 2
1 1
KAILASH SHARMA (REF-KAILASH10) 19 | P a g e
64. The work done in placing the dielectric slab inside one of the capacitors as
shown in the diagram.
2CV K 1
2 K -1
65. Two identical capacitors 1 and 2 are connected in series to a battery as shown in figure. Capacitor 2 contains a dielectric slab of dielectric constant k as shown. Q1 and Q2 are the charges stored in the capacitors. Now the dielectric slab is removed and the corresponding charges are Q’1 and Q’2 then
(A) 1
Q' K =
Q 2
66. The area of the plates of a parallel plate capacitor is A and the between them is d. The gap is filled with a non homogeneous dielectric whose dielectric constant
varies with the distance ‘y’ from one plate as K= λsec(πy/2d), where λ is a
dimensionless constant. The capacitance of this capacitor is
(A) πε0λ A/2d (B) πε0λ A/d (C) 2πε0λ A/d (D) none of these
67. Condenser A has a capacity of 15μF when it is filled with a medium of dielectric constant 15. Another condenser B has a capacity 1μF with air between the plates. Both are charged separately by a battery of 100 V. After charging, both
are connected in parallel without the battery and the dielectric material being removed. The common potential now is
(A) 400 V (B) 800 V (C) 1200 V (D) 1600 V
KAILASH SHARMA (REF-KAILASH10) 20 | P a g e
68. In the adjoining figure capacitor (1) and (2) have a capacitance ‘C’ each when
the dielectric of dielectric constant K is inserted between the plates of one of the
capacitor, the total charge flowing through battery is
(A) KCE
(B) KCE
(C) (K -- 1)CE
(D) −(K 1)CE
from C to B 2(K+1)
69. The distance between the plates of a charged parallel plate capacitor is 5cm and electric field inside the plates is 200 V cm–1. An uncharged metal bar of width 2cm is fully immersed into the capacitor. The length of the metal bar is
same as that of plate of capacitor. The voltage across capacitor after immersion
of the bar is
(A) zero (B) 400 V (C) 600 V (D) 100 V
KAILASH SHARMA (REF-KAILASH10) 21 | P a g e
Part-II Previous Year’s JEE Main Questions (2018-2020)
1. A parallel plate capacitor of capacitance 90 pF is connected to a battery of emf
20V. If a dielectric material of dielectric constant K = 5
3 is inserted between the
plates, the magnitude of the induced charge will be :
(A) 0.3 n C (B) 0.9 n C (C) 1.2 n C (D) 2.4 n C [JEE Main 2018]
2. The equivalent capacitance between A and B in the circuit given below, is
(A) 5.4 μF (B) 4.9 μF (C) 3.6 μF (D) 2.4 μF
[JEE Main Online 2018]
3. In the following circuit, the switch S is closed at t = 0. The charge on capacitor
C1 as a function of time will be given by
1 2 eq
C +C
(A) CeqE[1– exp(–t/RCeq)] (B) C1E[1– exp(–t/RC1)] (C) CeqE exp(–t/RCeq) (D) C2E[1– exp(–t/RC2)]
[JEE Main Online 2018]
4. A parallel palate capacitor with area 200 cm2 and separation between the plates 1.5 cm, is connected across a battery of emf V. If the force of attraction between

Nm
(A) 150 V (B) 100 V (C) 250 V (D) 300 V [JEE Main Online 2018]
KAILASH SHARMA (REF-KAILASH10) 22 | P a g e
5. A capacitor C1 = 1.0 μF is charged up to a voltage V = 60 V by connecting it to
battery B through switch (1). Now C1 is disconnected it to battery B through
switch connected to a circuit consisting of two uncharged capacitors C2 = 3.0 μF and C3 = 6.0 μF through switch (2), as shown in the figure. The sum of final charges on C2 and C3 is
(A) 20 μC (B) 40 μC (C) 36 μC (D) 54 μC [JEE Main Online 2018]
6. A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants K1, K2, K3, K4 arranged as shown in the figure. The effective
dielectric constant K will be:
(A) 1 2 3 4
1 2 3 4
2(K +K +K +K ) (B) 1 2 3 4
1 2 3 4
(K +K +K +K )
1 2 3 4
2(K +K +K +K ) (D) 1 3 2 4
1 2 3 4
(K +K +K +K )
[JEE Main 2019]
7. A parallel plate capacitor is of area 6 cm2 and a separation 3 mm. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants K1, = 10, K2 = 12 and K3 = 14. The dielectric constant of a
material which when fully inserted in above capacitor, gives same capacitance would be :
(A) 12 (B) 4 (C) 36 (D) 14
[JEE Main 2019]
KAILASH SHARMA (REF-KAILASH10) 23 | P a g e
8. A parallel plate capacitor having capacitance 12 pF is charged by a battery to a
potential difference of 10 V between its plates. The charging battery is now
disconnected and a porcelain slab of dielectric constant 6.5 is slipped between the plates the work done by the capacitor on the slab is :
(A) 692 pJ (B) 60 pJ (C) 508 pJ (D) 560 pJ [JEE Main 2019]
9. In the figure shown below, the charge on the left plate of the F capacitor is
–30C. The charge on the right place of the 6F capacitor is:
(A) –12 C (B) +12 C (C) –18 C (D) +18 C
[JEE Main 2019]
10. Seven capacitors, each of the capacitance 2F, are to be connected in a
configuration to obtain an effective capacitance of (6/13) F. Which of the combinations, shown in figures below, will achieve the desired value?
(A) (B)
(C) (D)
[JEE Main 2019]
11. In the figure shown, after the switch ‘S’ is turned from position ‘A’ to position ‘B’, the energy dissipated in the circuit in terms of capacitance ‘C’ and total charge ‘Q’ is:
(A) 21 Q
8 C (B)
KAILASH SHARMA (REF-KAILASH10) 24 | P a g e
12. In the circuit shown, find C if the effective capacitance of the whole circuit is to
be 0.5 F. All values in the circuit are in F.
(A) 7/11 F (B) 6/5 F (C) 4F (D) 7/10 F
[JEE Main 2019]
13. A parallel plate capacitor with plates of area 1 m2 each, are at a separation of 0.1 m. If the electric field between the plates is 100 N/C, the magnitude of charge on each plate is:
(A) 7.85 × 10-10 C (B) 6.85 × 10-10 C
(C) 8.85 × 10-10 C (D) 9.85 × 10-10 C [JEE Main 2019]
14. The charge on a capacitor plate in a circuit, as a function of time, is shown in the figure:
What is the value of current at t = 4 s?
(A) zero (B) 3 A (C) 2 A (D) 1.5 A [JEE Main 2019]
15. Voltage rating of a parallel plate capacitor is 500 V. Its dielectric can withstand a maximum electric field of 106 V/m. The plate area is 10–4 m2. What is the
dielectric constant if the capacitance is 15 pF? (given 0 = 8.86×10-12 C2 / Nm2)
(A) 6.2 (B) 4.5 (C) 3.8 (D) 8.5 [JEE Main 2019]
16. A parallel plate capacitor has 1F capacitance. One of its two plates is given
+2C charge and the other plate, +4C. The potential difference developed across the capacitor is:
(A) 1 V (B) 5 V (C) 3 V (D) 2 V
[JEE Main 2019]
KAILASH SHARMA (REF-KAILASH10) 25 | P a g e
17. A capacitor with capacitance 5µF is charged to 5µF. If the plates are pulled
apart to reduce the capacitance to 2µF, how much work is done?
(A) 3.75 × 10-6 J (B) 2.55 × 10-6 J (C) 6.25 × 10-6 J (D) 3.16 × 10-6 J [JEE Main 2019]
18. Determine the charge on the capacitor in the following circuit
(A) 10 µC (B) 200 µC (C) 60 µC (D) 2 µC
[JEE Main 2019]
19. The parallel combination of two air filled parallel plate capacitors of capacitance C and nC is connected to a battery of voltage, V. When the capacitors are fully
charged, the battery is removed and after that a dielectric material of dielectric constant K is placed between the two plates of the first capacitor. The new potential difference of the combined system is:
(A) V
nV
[JEE Main 2019]
20. Figure shows charge (q) versus voltage (v) graph for series and parallel combination of two given capacitors. The capacitances are :
(A) 50µF and 30µF (B) 60µF and 40µF (C) 40µF and 10µF (D) 20µF and 30µF
[JEE Main 2019]
KAILASH SHARMA (REF-KAILASH10) 26 | P a g e
21. Two identical parallel plate capacitors, of capacitance C each, have plates of
area A, separated by a distance d. The space between the plates of the two
capacitors is filled with three dielectrics, of equal thickness and dielectric constants K1, K2 and K3 .The first capacitor is filled as shown in fig. I, and the second one is filled as shown in fig II. If these two modified capacitors are charged by the same potential V, the ratio of the energy stored in the two, would be (E1 refers to capacitor (I) and E2 to capacitor (II)).
(A) ( )( )1 2 3 2 3 3 1 1 21
2 1 2 3
E K K K
2 1 2 3 2 3 3 1 1 2
K K KE =
E K +K +K K K +K K +K K
(C) ( )( )1 2 3 2 3 3 1 1 21
2 1 2 3
E 9K K K
2 1 2 3 2 3 3 1 1 2
9K K KE =
E K +K +K K K +K K +K K
[JEE Main 2019]
22. A parallel plate capacitor has plates of area A separated by distance 'd' between them. It is filled with a dielectric which has a dielectric constant that varies as k(x) = K(1 + αx) where 'x' is the distance measured from one of the plates. If
(αd) << 1, the total capacitance of the system is best given by the expression:
(A)
1+ d 2
KAILASH SHARMA (REF-KAILASH10) 27 | P a g e
23. A 60 pF capacitor is fully charged by a 20V supply. It is then disconnected from
the supply and is connected to another uncharged 60 pF capacitor in parallel.
The electrostatic energy that is lost in this process by the time the charge is redistributed between them is (in nJ) ________.
[JEE Main 2020]
24. Effective capacitance of parallel combination of two capacitors C1 and C2 is 10μF. When these capacitors are individually connected to a voltage source of
1V, the energy stored in the capacitor C2 is 4 times that of C1. If these capacitors are connected in series, their effective capacitance will be:
(A) 4.2 μF (B) 8.4 μF (C) 3.2 μF (D) 1.6 μF [JEE Main 2020]
25. A capacitor is made of two square plates each of side ‘a’ making a very small angle α between them, as shown in figure. The capacitance will be close to:
(A)
1 d 2d
[JEE Main 2020]
EXERCISE-II Part-I
Section-A
1. If Q is the charge on the plates of a capacitor of capacitance C, V the potential difference between the plates, A the area of each plate and d the distance between the plates, the force of attraction between the plates is
(A)
2
0
4 πε d
2. A capacitor C is charged to a potential difference V and battery is disconnected. Not if the capacitor plates are brought close slowly by some distance: (A) Some +ve work is done by external agent (B) Energy of capacitor will decrease (C) Energy of capacitor will increase (D) None of the above
3. Four capacitor s and a battery are connected as shown. The potential drop across the 7μF capacitor is 6V. Then the:
(A) potential difference across the 3 F capacitor is 10 V
(B) charge on the 3 F capacitor is 42 C (C) e.m.f of the battery is 30 V
(D) potential difference across the 12 F capacitor is 10 V
4. The capacitance of a parallel plate capacitor is C when the region between the plates has air. This region is now filled with a dielectric slab of dielectric
constant k. The capacitor is connected to a cell of emf E, and the slab is taken out
(A) Charge CE(k – 1) flows through the cell (B) Energy E2C(k – 1) is absorbed by the cell (C) The energy stored in the capacitor is reduced by E2C(k – 1)
(D) The external agent has to do 1
2 E2C(k – 1) amount of work to take the slab
out
KAILASH SHARMA (REF-KAILASH10) 29 | P a g e
5. A parallel plate air-core capacitor is connected across a source of constant
potential difference. When a dielectric plate is introduced between the two
plates then : (A) some charge from the capacitor will flow back into the source (B) some extra charge from the source will flow back into the capacitor (C) the average electric field intensity between the two plate does not change (D) the electric filed intensity between the two plates will decrease
6. A parallel plate capacitor of plate area A and plate separation d is charged to potential difference V and then the battery is disconnected. A slab of dielectric
constant K is then inserted between the plates of the capacitor so as to fill the space between the plates. If Q, E and W denote respectively, the magnitude of charge on each plate, the electric field between the plates (after the slab is inserted) and the work done on the system, in question, in the process of inserting the slab, then
(A) 0ε AV Q=
d (B) 0ε KAVQ=
2d K
7. The plates of a parallel plate capacitor with no dielectric are connected to a voltage source. Now a dielectric of dielectric constant K is inserted to fill the whole space between the plates with voltage source remaining connected to the capacitor (A) the energy stored in the capacitor will become K-times (B) the electric field inside the capacitor will decrease to K-times
(C) the force of attraction between the plates will increase to K2–times (D) the charge on the capacitor will increase to K–times
8. A parallel-plate capacitor is connected to a cell. Its positive plate A and its negative plate B have charges +Q and –Q respectively. A third plate C, identical to A and B, with charge +Q, is now introduced midway between A and B, parallel to them. Which of the following are correct?
(A) The charge on the inner face of B is now – 3Q
2
(B) There is no change in the potential difference between A and B
(C) The potential difference between A and C is one-third of the potential
difference between B and C
(D) The charge on the inner face of A in now Q/2
KAILASH SHARMA (REF-KAILASH10) 30 | P a g e
9. In the circuit shown in the figure, the switch S is initially open and the
capacitor is initially uncharged. I1, I2, and I3 represent the current in the
resistance 2, 4 and 8 respectively
(A) just after the switch S is closed, I1 = 3A, I2 = 3A and I3 = 0 (B) just after the switch S is closed, I1 = 3A, I2 = 0 and I3 = 0 (C) long time after the switch S is closed, I1 = 0.6A, I2 = 0 and I3 = 0 (D) long after the switch S is closed, I1 = I2 = 3 = 0.6A
10. The circuit shown in the figure consists of a battery of emf = 10 V; a capacitor
of capacitance C = 1.0 F and three resistor of values R1 = 2, R2 = 2 and
R3 = 1. Initially the capacitor is completely uncharged and the switch s is open. The switch S is closed at t = 0
(A) The current through resistor R3 at the moment the switch closed is zero (B) The current through resistor R3 a long time after the switch closed is 5A
(C) The ratio of current through R1 and R2 is always constant
(D) The maximum charge on the capacitor during the operation is 5C
KAILASH SHARMA (REF-KAILASH10) 31 | P a g e
11. In the circuit shown in figure C1 = C2 = 2F. Then at steady state
(A) capacitor C1 is zero (B) capacitor C2 is zero
(C) both capacitor is zero (D) capacitor C1 is 40 C
12. A capacitor of capacity C is charged to a steady potential difference V and connected in series with an open key and a pure resistor ‘R’. At time t = 0, the key is closed. If I = current at time t, a plot of log I against ‘t’ is as shown in (1)
in the graph. Later one of the parameters i.e. V, R or C is changed keeping the
other two constant, and the graph (2) is recorded. Then
(A) C is reduced (B) C is increased (C) R is reduced (D) R is increased
13. A parallel plate capacitor is connected to a battery. The quantities charge, voltage, electric field and energy associated with the capacitor are given by Q0, V0, E0 and U0 respectively. A dielectric slab is introduced between plates of capacitor but battery is still in connection. The corresponding quantities now given by Q, V, E and U related to previous ones are
(A) Q > Q0 (B) V > V0 (C) E > E0 (D) U < U0
KAILASH SHARMA (REF-KAILASH10) 32 | P a g e
Section-B
Paragraph for Qus 1 to 2
The charge across the capacitor in two different RC circuits 1 and 2 are plotted
as shown in figure.
1. Choose the correct statement(s) related to the two circuits.
(A) Both the capacitors are charged to the same charge (B) The emf’s of cells in both the circuit are equal (C) The emf’s of the cells may be different (D) The emf E1 is more than E2
2. Identify the correct statement(s) related to the R1, R2, C1 and C2 of the two RC
circuits. (A) R1 > R2 if E1 = E2 (B) C1 < C2 if E1 = E2
(C) R1C1 > R2C2 (D) 21
2 1
Paragraph for Qus 3 to 4
In the circuit as shown in figure the switch is closed at t = 0
3. At the instant of closing the switch
(A) The battery delivers maximum current (B) No current flows through C (C) Voltage drop across R2 is zero
(D) The current through the battery decreases with time finally becomes zero
KAILASH SHARMA (REF-KAILASH10) 33 | P a g e
4. A long time after closing the switch
(A) Voltage drop across the capacitor is E
(B) Current through the battery is 1 2
E
2
2
Section-C
[MATRIX TYPE]
1. In each situation of column-I, a circuit involving two non-ideal cells of unequal emf E1 and E2 (E1 > E2) and equal internal resistance r are given. A resistor of resistance R is connected in all four situations and a capacitor of capacitance C is connected in last two situations as shown. Assume battery can supply infinity charge to the circuit (r, R0, E1, E20). Four statements are given in column-II. Match the situation of column-I with statements in column-II.
Column-I Column-II
across both cells can never be same
(B)
that is, it gets charged up as long as
current flows in circuit
lower emf may be zero.
(D) The capacitor is initially uncharged.
After the key K is closed.
(S) current in the circuit can never be
zero (even after steady state is
reached).
KAILASH SHARMA (REF-KAILASH10) 34 | P a g e
2. Some events related to a capacitor are listed in column-I. Match these event
with their effect(s) is column-II.
Column-I Column-II
(P) Electric field between plates changes
(B) Removal of dielectric while battery is not present
(Q) Charge present on plates changes
(C) Slow decrease in separation
between plates while battery is attached
(R) Energy stored in capacitor
increases
between plates while battery is not present
(S) Work done by external agent is
positive
PART-II
(Subjective type Questions)
1. Both the capacitors shown in figure are made of square plates of edge a. The separations between the plates of the capacitors are d1 and d2 as shown in the figure. A battery of V volt and a resistance R are connected as shown in figure.
At steady state an electron is projected between the plates of the lower capacitor from its lower plate along the plate as shown. Minimum speed should
the electron be projected is given by
1/2 2
mdn so that it does not collide with
any plate ? Consider only the electric forces then find the value n.
2. In steady state, find the charge on the capacitor in (μC) shown in figure.
3. Find the potential difference between points A and B (in V) of the system shown in figure if the emf is equal to E = 110 V and the capacitance ratio C2/C1 = η = 2.0.
KAILASH SHARMA (REF-KAILASH10) 36 | P a g e
4. (i ) What is the final potential (in V) of point b with respect to ground in steady
state after switch S is closed ?
(ii) How much charge flows through switch S from b to a after it is closed in μC?
5. The equivalent capacitance of the combination shown in the figure between the
indicated points is given by n μF
7 . Then find the value of n.
6. The plates of a parallel plate capacitor are given charges +4Q and –2Q. The
capacitor is then connected across an uncharged capacitor of same capacitance as first one (=C). Find the final potential difference between the plates of the
first capacitor.
7. Find the equivalent capacitance of their circuit between point A and B.
KAILASH SHARMA (REF-KAILASH10) 37 | P a g e
8. Find heat produced in the circuit shown in the figure on closing the switch S.
9. In the following circuit, the resultant capacitance between A and B is 1µF. Find the value C.
10. Find the charges on the capacitor C = 1µF in the circuit shown in the figure,
KAILASH SHARMA (REF-KAILASH10) 38 | P a g e
11. In the circuit shown in figure R1 = R2 = 6R3 = 300 M, C = 0.01 µF and E =10v.
The switch is closed at t = 0, find
(a) Charge on capacitor a function of time.
(b) Energy of the capacitor at t = 20s
12. The two identical parallel plates are given charges as shown in figure. If the plate area of either face of each plate is A and separation between plates is d, then found the amount of heat liberate after closing the switch.
13. Three capacitor of 2µF, 3µF and 5µF are independently charged with batteries of emf’s 5V, 20V and 10V respectively. After disconnecting from the voltage
sources. These capacitors are connected as shown in figure with their positive polarity plates are connected to A and negative polarity is earthed. Now a
battery of 20V and an uncharged capacitor of 4µF capacitance are connected to the junction A as shown with a switch S. When switch is closed, find:
(a) The potential of the junction A.
(b) Final charges on all four capacitors.
KAILASH SHARMA (REF-KAILASH10) 39 | P a g e
14. In the circuit shown in figure, find the amount of heat generated when switch is
closed.
15. The connections shown in figure are established with the switch S open. How
much charge will flow through the switch if it is closed?
16. A 10µF and 20μF capacitor are connected to a 10 V cell in parallel for some
time after which the capacitors are disconnected from the cell and reconnected
at t = 0 with each other, in series, through wires of finite resistance. The +ve plate of the first capacitor is connected to the –ve plate of the second capacitor. Draw the graph which best describes the charge on the +ve plate of the 20µF capacitor with increasing time.
17. Two capacitors A and B with capacities 3µF and 2µF are charged to a potential difference of 100 V and 180V respectively. The plates of the capacitor are
connected as shown in figure with one wire from 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 Calculate :
(i) The final charges on the three capacitors (ii) The amount of electrostatic energy stored in the system before and after the completion of the circuit.
KAILASH SHARMA (REF-KAILASH10) 40 | P a g e
18. For the arrangement shown in the figure, the key is closed at t = 0. C2 is
initially uncharged while C1 has 2µC.
(a) Find the current coming out of the battery just after switch of closed (b) Find the charge on the capacitors in the steady state condition.
19. A potential difference of 300 V is applied between the plates of a plane capacitor speed 1cm apart. A plane parallel glass plate with a thickness of 0.5 cm and a plane parallel paraffin plate with a thickness of 0.5 cm are placed in the space between the capacitor plates find: (i) Intensity of electric field in each layer. (ii)The drop of potential in each layer.
(iii) The surface charge density of the charge on capacitor plates.
Given that: kglass= 6, kparaffin = 2
20. Five identical conducting plates 1, 2, 3, 4 & 5 are fixed parallel to and equidistant from each other (see figure). Plates 2 & 5 are connected by a conductor while 1 & 3 are joined by another conductor. The junction of 1 & 3 and the plate 4 are connected to a source of constant e.m.f. V0. Find;
(i) The effective capacity of the system between the terminals of the source. (ii) The charges on plates 3 & 5. [Given d= distance between any 2 successive plates & A = area of either
face of each plate.
21. Calculate the capacitance of a parallel plate condenser, with plate area A and

2
2
EXERCISE-III
1. Given : R1 = 1, R2 = 2, C1 = 2F, C2 = 4F
The time constants (in S) for the circuits I, II, III are respectively
(A) 18, 8/9, 4 (B) 18, 4, 8/9 (C) 4, 8/9 18 (D) 8/9, 18, 4
[JEE 2006]
2. A circuit is connected as shown in the figure with the switch S open. When the switch is closed, the total amount of charge that flows from Y to X is
(A) 0 (B) 54 C (C) 27 C (D) 81 C
[JEE 2007]
KAILASH SHARMA (REF-KAILASH10) 42 | P a g e
3. A parallel plate capacitor C with plates of unit area and separation d is filled
with a liquid of dielectric constant K = 2. The level of liquid is d
3 initially.
Suppose the liquid level decreases at a constant speed V, the time constant as
a function of time t is
(A) 06ε R
5d+3Vt (B)
[JEE 2008]
4. Statement-1: For practical, the earth is used as a reference at zero potential in electrical circuits.
Statement-2: The electrical potential of a sphere of radius R with charge Q
uniformly distributed on the surface is given by 0
Q
4πε R .
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct
explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is Not a correct
explanation for Statement-1 (C) Statement-1 is true, Statement-2 is false
(D) Statement-1 is false, Statement-2 is true
[JEE 2008]
KAILASH SHARMA (REF-KAILASH10) 43 | P a g e
5. At time t = 0, a battery of 10 V is connected across points A and B in the given
circuit. If the capacitors have no charge initially, at what time (in seconds) does
the voltage across them become 4 V? [Take : ln = 1.6, ln 3 = 1.1]
[JEE 2010]
6. A 2F capacitor is charged as shown in 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%
[JEE 2011]
7. In the given circuit, a charge of +80c is given to the upper plate of the 4 F
capacitor. Then in the steady state, the charge on the upper plate of the 3F capacitor is
(A) +32 C (B) +40 C (C) +48 C (D) +80 C
[JEE 2012]
KAILASH SHARMA (REF-KAILASH10) 44 | P a g e
8. In the circuit shown in the figure, there are two parallel plate capacitors each of
capacitance C. The switch S1 is pressed first to fully charge the capacitor C1
and then released. The switch S2 is then pressed to charge the capacitor C2. After some time, S2 is released and them S3 is pressed. After some time,
(A) The charge on the upper plate of C1 is 2CV0 (B) The charge on the upper plate of C1 is CV0 (C) The charge on the upper plate of C2 is 0
(D) The charge on the upper plate of C2 is –CV0 [JEE 2013]
9. A parallel plate capacitor has a dielectric slab of dielectric constant K between
its plates that covers 1
3 of the area of its plates, as shown in the figure. The
total capacitance of the capacitor is C while that of the portion with dielectric in between is C1. When the capacitor is charged, the plate area covered by the dielectric gets charge Q1 and the rest of the area gets charge Q2. The electric field in the dielectric is E1 and that in the other portion is E2. Choose the correct option/options, ignoring edge effects.
(A) 1
KAILASH SHARMA (REF-KAILASH10) 45 | P a g e
10. A parallel plate capacitor having plates of area S and plate separation d, has
capacitance C1 in air. When two dielectrics of different relative permittivity
(1 = 2 and 2 = 4) are introduced between the two plates as shown in the figure,
the capacitance becomes C2. The ratio 2
1
C
[JEE 2015]
11. In the circuit shown-below, the key is pressed at time t = 0. Which of the following statement(s) is(are) true?
(A) The voltmeter displays –5 V as soon as the key is pressed, and displays +5
V after a long time
(B) The voltmeter will display 0 V at time t = ln 2 seconds (C) The current in the ammeter becomes 1/e of the initial value after 1 second
(D) The current in the ammeter becomes zero after a long time [JEE 2016]
KAILASH SHARMA (REF-KAILASH10) 46 | P a g e
Paragraph for Question Nos. 12 to 13
Consider an evacuated cylindrical chamber of height h having rigid conducting plates at the ends and an insulating curved surface as shown in the figure. A number of spherical balls made of a light weight and soft material and coated with a conducting material are placed on the bottom plate. The balls have a
radius r << h. Now a high voltage source (HV) is connected a cross the conducting plates such that the bottom plate is at + V0 and the top plate at –V0. Due to their conducting surface, the balls will get charged, will become equipotential with the plate and are repelled by it. The balls will eventually collide with the top plate, where the coefficient of restitution can be taken to be
zero due to the soft nature of the material of the balls. The electric field in the
chamber can be considered to be that of a parallel plate capacitor. Assume that there are no collisions between the balls and the interaction between them is negligible. (Ignore gravity)
12. Which one of the following statements is correct? (A) The balls will bounce back to the bottom plate carrying the same charge
they went up with
(B) The balls will bounce back to the bottom plate carrying the opposite charge
they went up with
(C) The balls will stick to the top plate and remain there
(D) The balls will execute simple harmonic motion between the two plates
[JEE 2016]
13. The average current in the steady state registered by the ammeter in the circuit will be
(A) Proportional to the potential V0 (B) Proportional to 1/2
0V
0V
KAILASH SHARMA (REF-KAILASH10) 47 | P a g e
14. A parallel place capacitor of capacitance C has spacing d between two plates
having area A. The region between the plates is filled with N dielectric layers,
parallel to its plates, each with thickness d
δ = N
mth layer is
m K =K 1+

[ε0 is the permittivity of free space
[JEE 2019]
15. Two capacitors with capacitance values C1 = 2000 ± 10 pF and 2 = 3000 ± 15 pF are connected in series. The voltage applied across this combination is
= 5.00 ± 0.02 V. The percentage error in the calculation of the energy stored in this combination of capacitors is _______.
[JEE 2020]
Part-I Section A to E
1. A 2. D 3. B 4. B 5. A 6. C 7. B 8. C 9. D 10. A
11. C 12. B 13. B 14. C 15. D 16. D 17. C 18. (i)-B; (ii)- C 19. A
20. D 21. D 22. A 23. B 24. A 25. D 26. B 27. A 28. A 29. C
30. B 31. A 32. A 33. C 34. B 35. B 36. C 37. C 38. C 39. B
40. B 41. B 42. B 43. C 44. A 45. D 46. C 47. D 48. A 49. A
50. D 51. C 52. D 53. D 54. B 55. A 56. B 57. B 58. A 59. A
60. B 61. A 62. B 63. D 64. B 65. C 66. A 67. B 68. D 69. C
Part-II Previous Year’s Question (2019-2020)
1. C 2. D 3. A 4. C 5. B 6. D 7. A 8. C 9. D 10. B
11. B 12. A 13. C 14. A 15. D 16. A 17. A 18. B 19. B 20. C
21. D 22. B 23. 6 24. D 25. A
EXERCISE-II
PART-I
Section-A
1. AB 2. B 3. BCD 4. ABD 5. BC 6. ACD 7. ACD 8. ABCD
9. B 10. ABCD 11. BD 12. D 13. A
Section-B
Section-C
1. (A)-PQS (B)-PRS (C)-PQ (D)-PR 2. (A)-QR; (B)-PRS; (C)-PQR; (D)-RS
KAILASH SHARMA (REF-KAILASH10) 49 | P a g e
PART-II
1. 6 2. 6 3.10 4. (i) 6 (ii) 54 5. 20μF
6. 3Q/2C 7. C 8. 0 9. 32
μF 23
10. 10μC
11. (a) q = 0.05 (1 – e–t/2) μC; (b) 0.125 μJ 12.
2
0
13. (a) 100
7 volts; (b) 28.56 μC, 42.84 μC, 71.4 μC, 22.88 μC
14. 150 mJ 15. 12 μC 16. Graph
17. QA = 90μC, QB = 150 μC, QC = 210 μC, Ui = 47.4 mJ, Uf = 18 mJ]
18. (a) 7
, (b) Q1= 9 μC, Q2 = 0
19. (i) 1.5× 104 V/m, 4.5 ×104V/m, (ii) 75 V, 225V, (iii) 8×10-7C/m2
20. (i)
0 A5 ;