hii ! ! ! ! ! !

 

Consider a capacitor of capacitence C and is charged at potential diff. V  . The charge stored in the capacitor is given by

 

Q = CV

 

V = Q/C.....(1)

 

Let the capacitor is given a very small charge dQ by a battery at const. potential V , the amt of work done is given by

 

dW= (dQ)V

 

dW = Q/C .dQ

total work done in charging the capacitor is given by

 

 

_{[ ]}^{[ ]} dW = _{[ 0]}^{[ Q]}Q/C.dQ = 1/C (Q²/2) FRM 0 TO Q

 

 

W = 1/2 Q² / C

 

this work done in tyhe capacitor is in the form of potential energy

 

U = 1/2 . Q² / C

 

Q = CV

 

U = 1/2 C² V² / C = 1/2CV²

 

C = Q/V

 

U = 1/2 Q.V² / V

 

U = 1/2 QV

 

 

SO

 

U = 1/2 CV² = 1/2Q² /C = 1/2 QV