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derive an expression for the energy stored in a capacitor with Air as the medium between its plates.how does the stored energy change if Air is replaced by a medium of dielectric constant k


byabangtaking19 25th Oct, 2020
Answer (1)
gauravvijayvargiya399 26th Oct, 2020

Let us consider a capacitor of capacitance C and potential difference V between the plates.

Let the charge on one plate be +q and -q on the other.

Suppose the capacitor is being charged gradually.

Now,at any stage the charge on capacitor is q.

Therefore, the potential difference =  q/C

Small amount of work done in giving n additional charge dq to the capacitor is =

dW = C/q × dq

Total work done in giving a charge Q to the capacitor  is

W=∫dW  ~~~~~~ (A) equation

Now, by putting the value of dW = C/q × dq in above equation (A) and integrating it and putting values of upper limit = Q and lower limit = 0 and thus integrating the whole equation we get,

W = Q^2/ C

Here let Energy= E

E= Q^2/ 2C

= C V^2 / 2

= QV/2

The energy is stored in the form of potential energy.

Hope that helps

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