Question

Wo large conducting parallel plates having equal charge q are placed very close to each other and distance between the plates is d. Find the work done by external agent to increase the separation between plates by d (area of plate is a)

Answer 1

When capacitors are connected in parallel, the total capacitance is the sum of the individual capacitors' capacitances. If two or more capacitors are connected in parallel, the overall effect is that of a single equivalent capacitor having the sum total of the plate areas of the individual capacitors.

Answer 2

Correct Question:-

The plate separation in a parallel plate capacitor is d and plate area is A. If it is charged to V volts then calculate the work done in increasing the plate separation to 2d.

The work done by external agent to increase the separation between plates by d is EoAV²/2d.

Given:-

Distance of separation of plates = d

Area of cross section of plate = A

Voltage on the plate = V

To Find:-

The work done by external agent to increase the separation between plates by d.

Solution:-

We can easily find out the work done by external agent to increase the separation between plates by d by using these simple steps.

As

Distance of separation of plates = d

Area of cross section of plate = A

Voltage on the plate = V

Charge = q

Capacitance of Capacitor = c

So, according to the formula of charge,

$q = c \times v$

and, Capacitance is given by

$c = \frac{EoA}{d}$

on putting this value of capacitance in the above equation, we get

$q = ( \frac{EoA}{d} ) \times v$

In question it is mentioned that charging of a capacitor,. which makes the charge constant.

So,

$w = uf - ui$

$w = \frac{ {q}^{2} }{2cf} - \frac{ {q}^{2} }{2ci}$

$w = \frac{ {q}^{2} }{2} ( \frac{1}{cf} - \frac{1}{ci} )$

in the above equation, let us put the value of q and c.

Then,

$w = \frac{( { \frac{EoA}{d}) }^{2} }{2} ( \frac{2d}{EoA} - \frac{d}{EoA} )$

on solving the above equation, we get

$w = \frac{EoA {v}^{2} }{2d}$

Hence, The work done by external agent to increase the separation between plates by d is EoAV²/2d.

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