Capacitors and Dielectrics | Visual Physics for IIT JEE / NEET
Introduction

Overview of a Battery

Capacitor

What is a Capacitor ? How do we define Capacitance ? Are there different types of capacitors ?

Parallel Plate Capacitor

Derivation of Capacitance of a Parallel Plate Capacitor

Q1

In figure, an uncharged capacitor of capacitance C = 2 mF is connected to the battery of potential difference V = 10 V. The capacitor plates have an area A = 4 x 10-4 m2, and the density of conduction electrons in the metal is r = 9 x 1028 electron/m3. Find the depth within the plate from which the electrons move to the surface of plates as the capacitor becomes charged?

Cylindrical Capacitor

Derivation of Capacitance of a Cylindrical Capacitor

Q2

The cross section of a cable of length 11 km is shown in figure. The inner cylinder has a radius of 2 cm and outer cylinder has a radius of 6 cm. Space between them is filled with a dielectric with dielectric constant of 9. Potential difference between the inner and outer cylinder is 240 volts. What is the capacitance and the charge of the cable. ( given loge 3 = 1.1 )

Spherical Capacitor

Derivation of Capacitance of a Spherical Capacitor. Derivation of Capacitance of a Conducting isolated charged sphere.

Q3

A spherical capacitor has an inner sphere of radius 9 cm and an outer sphere of radius 16 cm. The outer sphere is earthed and the inner sphere is given a charge of 32 pC. The space between the concentric spheres is filled with a liquid of dielectric constant 7. Determine the potential of the inner sphere. a) 10 V b) 20 V c) 30 V d) 40 V

Energy Stored in Capacitor

Derivation of the energy stored in capacitor. Derivation of the electrostatic energy density.

Q4

A photographic flash uses an average power of 1000 W for 0.25 s. The flash is due to discharge of a fully charged capacitor of 20 mF. The voltage to which the capacitor is charged before connecting to the flash is

Q5

An isolated conducting sphere with radius R has a charge Q on it. a) How much potential energy is stored in the electric field of this charged sphere ? b) What is the energy density near the surface of sphere ?

Q6

A parallel-plate capacitor of capacity Co is charged to a potential Vo. The separation between the plates is doubled, for two cases a) after the capacitor is disconnected b) while the battery remains connected Find the ratio of Charge, Potential, Field and Energy stored in the capacitor in the two cases.

Q7

Figure shows two thin conducting shells of radius ?a? and b. Initially, switches S1, S2, and S3 are open and the inner shell carries a charge Q. First, switch S1 is closed to connect outer shell with ground, and then S1 is opened. Now, switch S2 is closed so that inner shell is grounded and then S2 is opened. Finally, switch S3 is closed to connect the shells together. Find the heat produced on closing switch S3.

Series Parallel - 1

Equivalent capacitance of the combination of capacitors in Parallel combination. Is energy stored in equivalent capacitor equal to the total energy stored in all capacitors connected in parallel ?

Series Parallel - 2

Equivalent capacitance of the combination of capacitors in Series combination. Is energy stored in equivalent capacitor equal to the total energy stored in all capacitors connected in series ?

Q8

Three capacitors are connected across a battery as shown in figure. a) Find equivalent capacitance b) Find potential difference and charge on each capacitor c) Find energy stored in each capacitor and d) Total energy stored in the system of capacitors

Q9

For the system of capacitors shown in figure, find a) charge, potential difference and energy stored in each capacitor, b) total charge and energy stored in system A capacitor of 1 mF is now connected between points A and B. c) Is there any change in charge or energy stored in the original circuit ? d) What is the new total charge and energy stored in system

Q10

What is the equivalent capacitance of the circuit between the points A and B ?

Q11

Find the equivalent capacitance between points A and B.

Q12

In the system shown in figure, Find a) The potential difference across each capacitor b) Charge stored in each capacitor

Loop Law - 1

Loop Law for Circuits

Loop Law - 2

Loop Law for Circuits

Q13

For the network of capacitors shown in figure, find the potential of junctions A, B, C and D

Q14

Two condensers C1 and C2 in a circuit are joined as shown figure. The potential of point A is VA and that of B is VB. The potential of point D will be

Q15

In the circuit shown in figure. C = 4 mF. The charge stored in the capacitor of capacity C is a) 90 mC b) 80 mC c) 60 mC d) zero

Q17

A capacitor can store any amount of charge. True / False ?

Q18

Figure shows two identical parallel-plate capacitors connected to a battery with the switch S closed. The switch is now opened and the free space between the plates of the capacitors is filled with a dielectric of dielectric constant (or relative permittivity) K = 3. Find the ratio of the electrostatic energy stored in each capacitor before and after the introduction of the dielectric.

Q19

When a thick metal plate of thickness t is placed between the plates of a parallel-plate capacitor, capacitance.... a) increases b) decreases c) remains the same d) cannot be determined

Q20

A parallel-plate capacitor with no dielectric has a capacitance of C mF. The space between the plates is filled with two dielectric slabs of equal thickness and dielectric constants K1 and K2 as shown in figure. Find the capacitance of the system in each case.

Q21

A capacitor of capacitance C1 = 2 mF can withstand a maximum voltage of V1 = 9 kV and another capacitor of capacitance C2 = 3 mF can withstand a maximum voltage of V2 = 7 kV. If they are connected in series, what maximum voltage can the system withstand?

Q22

A parallel-plate capacitor contains a mica sheet ( thickness 10-3 m ) and a sheet of fiber ( thickness 2 10-3 m ). The dielectric constant of mica is 8 and that of fiber is 3. Assuming that the fiber breaks down when subjected to an electric field of 6 106 Vm-1, find the maximum safe voltage that can be applied to the capacitor.

Q23

a) Capacitance of capacitor becomes 4/3 times its original value if a dielectric slab of thickness t = d/3 is inserted between the plates (separation between the plates is = d). What is the dielectric constant of the slab ? b) If two such slabs are inserted in the capacitor then the capacitance is 3/2 times the capacitance when one slab was inserted. What is the dielectric constant of the slab ?

Q24

We have a sheet of Dielectric 1 ( thickness = 0.10 cm, K = 5 ) Dielectric 2 ( thickness = 0.20 cm, K = 7 ) Dielectric 3 ( thickness = 0.30 cm, K = 9 ) To obtain the largest capacitance, which sheet should you place between the copper plates, if the distance between the plates a) is kept equal to the thickness of slab ? b) is kept at a fixed value (say 1 cm) ?

Q25

Two identical capacitors are connected as shown figure. One of the operations listed in Column 1 is done independently on one of the capacitors. Mark the corresponding effects listed in Column 2. a) Separation between plates increased b) A dielectric slab is inserted c) A metal plate is inserted between the plates 1) Change on the system increases 2) Change on the system decreases 3) Energy stored in the system increases

1

Find the capacitance of systems shown in figure ?

2

The first slab in the figure is a conductor and the second slab is a dielectric with dielectric constant = K. Draw the graph of change in potential.

3

A charged parallel plate capacitor is placed such that its top plate is fixed, whereas the bottom plate is kept in equilibrium by the gravitational and electrostatic forces. a) When the capacitor is isolated, the plate is in unstable equilibrium b) When the capacitor is isolated, the plate is in neutral equilibrium c) When the capacitor is connected to a battery , the plate is in unstable equilibrium d) When the capacitor is connected to a battery , the plate is in neutral equilibrium

4

Which of following graph in figure represents the force between plates vs the distance between the plates for a) an isolated charged parallel - plate capacitor b) a parallel - plate capacitor which remains connected to battery

5

A capacitor is made of a flat plate of area 3A and a second plate having a stair like structure as shown in figure. The area of each stair is A and the height is d. Find the capacitance of this arrangement.

6

A capacitor has rectangular plates of width a and depth b. The second plate is inclined at a small angle q as shown in figure. Find the capacitance of this system.

7

For the system of capacitors shown in the figure, if charge on 3 mF capacitor is 30 mC, find the potential difference between points M and N.

8

In the circuit shown in figure, the potential difference between the points A and B is 9 V. Find the e.m.f. of the battery. Capacitances indicated are in mF

9

Two non - conducting spheres of radius a and b are separated by a distance d as shown in figure. Capacitance of system is

10

The plates of a parallel-plate capacitor are charged up to V. Now, after removing the battery, a dielectric slab of thickness t is inserted between the plates. Then to maintain the same potential difference, distance between the capacitor plates is increased by Dd. Find the expression for dielectric constant of the slab in terms if t and Dd

11

Two parallel-plate capacitors of capacitance C each are connected in a) parallel b) series with a battery of e.m.f V. Then, one of the capacitors is filled with a dielectric of dielectric constant K. Find the change in equivalent capacitance, total charge on capacitors, potential difference across each capacitor, electric field in each capacitor and energy stored in the two capacitors, if any.

12

The capacitance of an infinite circuit formed by the repetition of the same link consisting of two identical capacitors, each with capacitance C.

13

The capacitors in figure are initially uncharged and the switch is open. The applied potential difference is VAB = +300 V a) What is the potential difference VCD ? b) What is the potential difference across each capacitor after switch is closed ? c) How much charge will flow through the switch after it is closed ?

14

When the switch is closed, what amount of charge will flow through the battery ? What amount of charge will flow through the switch ?

15

Find the equivalent capacitance between points A and B shown in figure.

16

Four identical metal plates, each with a surface area A, are placed at a distance d from each other as shown in figure. The two inner plates are connected to point B and the other two plates are connected to point A. Capacitance of the system is ?

17

Four identical metal plates are kept at equal distance d from each other. The area of each plate is A. A battery with potential difference V is connected across the inner plates and outer plates are connected by a metal wire. Discuss the charge distribution and find the capacitance of the system.

18

Identical metal plates with area A are placed at distances as shown in the figure. Find the capacitance of the system.

19

Three plates with area A and separation d between them are arranged as shown in the figure. What is the energy stored in system ?

20

Five identical conducting plates a, b, c, d, e are parallel and equidistant from each other and are connected as shown in the figure. Find a) the effective capacitance of the system between the terminals of battery b) and charge on each plate

21

A capacitor of capacitance C is charged to a potential difference Vo. The terminals of the charged capacitor are then connected to those of an uncharged capacitor of capacitance C/2. Compute a) the initial charge of the system b) the final charge and potential difference across each capacitor c) the decrease in energy when the capacitors are connected

22

An uncharged parallel-plate capacitor having a dielectric of dielectric constant K is connected to a similar air cored parallel-plate capacitor charged to a potential V0. The two share the charge and the common potential becomes V. The dielectric constant K is

23

A capacitor of capacitance C1 = 1 mF charged up to a voltage V = 60 V and then connected to two uncharged capacitors connected in series with capacitance C2 = 3 mF and C3 = 6 mF. The amount of charge that will flow through the connecting wires is a) 20 mC b) 40 mC c) 60 mC d) 100 mC

24

Capacitor A is initially charged to store 1200 J of energy. It is then connected to the capacitors B and C as shown in figure. What is the final potential difference across capacitor A ?

25

In figure, 2 mF capacitor is intially charged to a potential of 200 V. It is then connected to the 3 mF and 5 mF capacitor as shown. When equilibrium is reached, find the charge on each capacitor ?

26

Two capacitors C1 and C2 are charged to the same initial potential difference. The charged capacitors are removed from the battery and their plates are connected as shown in the figure. a) What is the final potential difference across the capacitors ? b) Find the total energy stored in the capacitors before and after they are connected and the ratio of the final energy to the initial energy.

27

A 2 mF and a 3 mF capacitor are connected in series across a 1000 V supply. The charged capacitors are disconnected and are now reconnected, with terminals of a) like sign together b) opposite sign together Find the final charge on each capacitor and voltage across them.

28

Two capacitors A and B with capacities 3 mF and 2 mF are charged to a potential difference of 100 V and 180 V, respectively. Plates of the capacitors are connected as shown in figure (upper plate of A is positive and that of B is negative). An uncharged 2 mF capacitor is then connected to the capacitors to complete the circuit. Calculate a) The final charge on the three capacitors, b) The amount of electrostatic energy stored in the system before and after the completion of the circuit.

29

Capacitors with capacitance C, 2 C, 3 C and 4 C are charged to the voltage V, 2 V, 3 V and 4 V, respectively, and then connected as shown in the figure. When the switches are closed, find the voltage across all capacitors.

30

A capacitor of capacitance C is charged by connecting it to a battery of emf V. the capacitor is now disconnected and reconnected to the battery with the polarity reversed. Calculate the heat dissipated in connecting wires

31

A capacitor of capacitance Co is charged to a potential Vo and then isolated. A capacitor C is then charged from Co, discharged and charged again. This process is repeated n times. Find the potential and charge on first capacitor after n cycles.

32

Find the potential difference between the points M and N and charge and potential difference of C1

33

Find the equivalent capacitance of the circuit shown in figure.

34

For the circuit shown in figure a) The charge on C1 and C2 are same b) The charge on C2 is greater that on C1 c) The potential drops across C1 and C2 are the same d) The potential drops across C1 is greater then that acrossC2

35

What charge will flow through sections A, B and C of the circuit when switch is closed ?

36

Three capacitors A, B, and C are connected in a circuit as shown in figure. What is the charge in mC on the capacitors B?

37

Four large parallel thin metallic plates are placed as shown in figure. Find the potential difference between the inner plates.

38

A capacitor of capacitance C is charged to a potential difference V from a battery and then disconnected from it. A charge +Q is now given to its positive plate. Find the potential difference across the capacitor.

39

Plate A has positive charge Q1 and plate B has charge Q2. A battery of e.m.f. V has its positive terminal connected to plate A and negative terminal to plate B. If capacitance is given to be C, find the charge supplied by the battery.

40

Three identical large metallic plates are placed parallel to each other at very small separation as shown in fig. The central plate is given a charge Q. What amount of charge will flow to earth when key is pressed ?

41

In the arrangement shown in figure, plate B is given a charge equal to 60 mC. Distance between AB is d and distance between BC is 2d. Find the charge on each surface.

42

In figure when switch is swapped from 1 to 2 Find the heat produced in the circuit.

43

Two parallel-plate capacitors A and B have the same separation d = 8.85 X 10-4 m between the plates. The plate areas of A and B are 0.04 m2 and 0.02 m2, respectively. A slab of dielectric constant K ( = 9 ) has dimensions such that it can exactly fill the space between the plates of capacitor B. Initially dielectric slab is placed inside A as shown in figure - 1. A is charged to a potential difference of 110 V. a) Calculate the capacitance of A and the energy stored in it. The battery is then disconnected and the dielectric slab is removed from A. b) Find the work done by the external agent in removing the slab from A. The same dielectric slab is now placed inside B, filling it completely. The two capacitors A and B are then connected as shown figure - 2. c) Calculate the energy stored in the system

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