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A parallel plate capacitor of capacitance C is connected to a battery and is charged to a potential difference V.

Another capacitor of capacitance 2C is connected to another battery and is charged to potential difference 2V. The charging batteries are now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is

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Important Questions on Capacitance

EASY

Physics>Electricity and Magnetism>Capacitance>Capacitance

A parallel plate capacitor is of area

6 c m^{2}

and a separation

3 m m .

The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constant

K_{1} = 10, K_{2} = 12

and

K_{3} = 14 .

The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be:

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HARD

Physics>Electricity and Magnetism>Capacitance>Capacitance

A parallel plate capacitor having cross-sectional area $A$ and separation $d$ has air in between the plates. Now an insulating slab of the same area but the thickness, $\frac{d}{2}$ , is inserted between the plates as shown in figure having dielectric constant $K (= 4) .$ The ratio of new capacitance to its original capacitance will be,

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MEDIUM

Physics>Electricity and Magnetism>Capacitance>Capacitance

A parallel plate capacitor of two plates, each with area $90 π {cm}^{2}$ , is separated by $5 mm$ air-gap. The capacitor is initially connected to $100 V$ source. When an unknown liquid is filled between the plates so as to fill the air-gap, an additional charge of $95 nC$ is found to be flowing onto the capacitor from the $100 V$ source. The dielectric constant of the liquid is
(Assume $\frac{1}{4 π ϵ_{0}} = 9 \times 10^{9} N m^{2} C^{- 2}$ )

EASY

Physics>Electricity and Magnetism>Capacitance>Capacitance

A parallel plate capacitor with plates of area

1 m^{2}

each, are at a separation of

0.1 m .

If the electric field between the plates is

100 N C^{- 1},

the magnitude of charge on each plate is:

(Take ε_{0} = 8.85 \times 10^{- 12} C^{2} N^{- 1} m^{- 2})

EASY

Physics>Electricity and Magnetism>Capacitance>Capacitance

A parallel plate capacitor has

1 μ F

capacitance. One of its two plates is given

+ 2 μ C

charge and the other plate,

+ 4 μ C

charge. The potential difference developed across the capacitor is:

EASY

Physics>Electricity and Magnetism>Capacitance>Capacitance

For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant

K

is used, which has the same area as the plates of the capacitor. The thickness of the dielectric slab is

\frac{3}{4} d

, where

d

is the separation between the plates of parallel plate capacitor. The new capacitance

C^{'}

in terms of original capacitance

C_{0}

is given by the following relation :

MEDIUM

Physics>Electricity and Magnetism>Capacitance>Capacitance

In a parallel plate capacitor, the capacity can be increased by decreasing

MEDIUM

Physics>Electricity and Magnetism>Capacitance>Capacitance

A spherical capacitor consists of two concentric spherical conductors. Find the capacitance of the spherical capacitor if the outer radius is

2 R

and the inner radius is

R .

MEDIUM

Physics>Electricity and Magnetism>Capacitance>Capacitance

Two thin dielectric slabs of dielectric constants

K_{1}

and

K_{2} (K_{1} < K_{2})

are inserted between plates of a parallel plate capacitor, as shown in the figure. The variation of electric field ‘

E

’ between the plates with distance ‘

d

’ as measured from plate

P

is correctly shown by:
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HARD

Physics>Electricity and Magnetism>Capacitance>Capacitance

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:
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EASY

Physics>Electricity and Magnetism>Capacitance>Capacitance

Eight drops of mercury of equal radii combine to form a big drop. The capacitance of a bigger drop as compared to each smaller drop is

HARD

Physics>Electricity and Magnetism>Capacitance>Capacitance

A parallel plate air capacitor of capacitance

C

is connected to a cell of emf

V

and then disconnected from it. A dielectric slab of dielectric constant

K

, which can just fill the air gap of the capacitor, is now inserted in it. Which of the following is incorrect?

HARD

Physics>Electricity and Magnetism>Capacitance>Capacitance

If a slab of insulating material,

4 \times 10^{- 3} m

thick is introduced between the plates of a parallel plate capacitor, the separation between the plates has to be increased by

3.5 \times 10^{- 3} m

to restore the capacity to original value. The dielectric constant of the material will be

HARD

Physics>Electricity and Magnetism>Capacitance>Capacitance

How will the voltage

(V)

between the two plates of a parallel plate capacitor depend on the distance

(d)

between the plates, if the charge on the capacitor remains the same?

EASY

Physics>Electricity and Magnetism>Capacitance>Capacitance

Four metallic plates each of area $A$ and separated from one another by a distance $d$ are arranged as shown in the figure. What is the capacitance between $X$ and $Y ?$

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EASY

Physics>Electricity and Magnetism>Capacitance>Capacitance

What happens to the capacitance of a parallel plate capacitor if the area of its plate is tripled?

EASY

Physics>Electricity and Magnetism>Capacitance>Capacitance

Consider a spherical drop of mercury of radius

R

with capacitance

C = 4 π ε R .

If two such droplets combine to form a larger one, what would be its capacitance in terms of

C

HARD

Physics>Electricity and Magnetism>Capacitance>Capacitance

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_{0} (1 + α x)

where

x

is the distance measured from one of the plates. If

(α d) < < 1,

the total capacitance of the system is best given by the expression:

HARD

Physics>Electricity and Magnetism>Capacitance>Capacitance

A parallel plate capacitor is made of two circular plates separated by a distance of 5 mm and with a dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is $3 \times 1 0^{4} V/m$ , the charge density of the positive plate will be close to :

EASY

Physics>Electricity and Magnetism>Capacitance>Capacitance

In the figure is shown a system of four capacitors connected across a $10 V$ battery. The charge that will flow from switch S when it is closed is:
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Important Questions on Capacitance

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