Define capacitance of capacitor? Derive relation for energy stored in capacitor when it is charged to potential difference of V volts.

Capacitance Long Question Solution

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Define capacitance of capacitor? Derive relation for energy stored in capacitor when it is charged to potential difference of V volts.

Capacitance - Long Question Answer 1

Question: What is capacitance of capacitor? Derive the relation for the energy stored in a capacitor when it is charged to a potential difference of V volts.

Answer: Capacitance of a capacitor defines as the ability of a capacitor to store charge is called its capacitance. The rise in potential difference between conducting plates is directly proportional to the charge given to them i.e. q α V => q = C V

Where C is constant of proportionality called capacitance of a conductor. Thus,

C = q/v

When v = 1volt, then C = q

Thus, capacitance of a capacitor is numerically equal to the charge required to rise P.D. by 1 volt. The SI unit of capacitance is Farad (F).

Energy stored in a charged capacitor: Suppose an uncharged capacitor of capacitance C is to be charged with charge Q till the potential difference becomes V, then q = C V

When the capacitor is being charged let dq be charge at any instant and P.D. across the plate is V.

Then the work done by the charge on charging it is given by, dW = V dq, Since q = C V, V = q/C,

SO, dW = q/C dq

Integrating both sides from 0 to q as limits,

qʃ0dW = C qʃq dq

or, W = C [q2/2]0q

or, W = q2/2C

This work done is stored as (electrical potential) energy on the capacitor. Thus, energy stored in the capacitor is given by,

E = q2/ 2C

Moreover, using q = C V, we get

E = (CV)2 / 2C = ½ CV2

and

E = (½ q) / (q/V)      

E = ½ q V

Hence, E = ½ qV = ½ (CV)2 =q2/ 2C

This is the required expression of energy stored by capacitor.

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