Question

For capacitors charged by the same battery,
does the charge stored by the capacitors increase, decrease or remain the same in each of the following situations?
A) the plate separation of The parallel plate capacitor is increased.
B) in the radius of the inner cylinder of a cylindrical capacitor is increased.
C) the radius of the outer spherical shell of a spherical capacitor is increased.



12th std
Ch. Electrostatic potential and capacitance. ​

Answer 1

Given that,

Capacitors charged by the same battery

(A). If the plate separation of The parallel plate capacitor is increased

We know that,

The formula of capacitor is

$C=\dfrac{\epsilon A}{d}$

Where, A = area

d = separation

C = capacitor

If the plate separation is increased, then the capacitance will decrease.

According to charge formula,

$Q=CV$

Where, C = capacitor

V = voltage

Q = charge

So, The capacitor is decreased then the charge will be decrease and potential will remain constant.

(B). If in the radius of the inner cylinder of a cylindrical capacitor is increased

When the radius is increased, then the area will increases and hence the capacitance will also increase.

So, the charge stored by the capacitors increase and voltage is constant.

(C). If the radius of the outer spherical shell of a spherical capacitor is increased.

We know that,

$C=\dfrac{4\pi\epsilon r_{o}r_{in}}{r_{o}-r_{in}}$

The radius of the outer spherical shell is increased then capacitor will increased.

So, the charge stored by the capacitors will increase.

Hence, (A). The charge stored by the capacitors will increase.

(B). The charge stored by the capacitors will increase.

(C). The charge stored by the capacitors will increase.