A condenser of certain capacity is charged to a potential V and stores some energy. A second condenser of twice the capacity is to store half the energy of the first , find to what potential one must be charged ?

Explanation

For first capacitor , `C_1=C,V_1=V`
And `U_1=(1)/(2)C_1V_(1)^(2)=(1)/(2)CV^2`............. (1)
For second capacitor , `C_2=2C_1=2C`,
`U_2=(U_1)/(2)=(1)/(4)CV^2`, Let potential difference across the capacitor `=V_2`

Then `U_2=(1)/(2)C_2V_(2)^(2)`
`rArr (1)/(4)CV^2=(1)/(2)xx2CxxV_(2)^(2)`
`rArr V_(2)^(2)=(V^2)/(4)`
`therefore V_2=(V)/(2)` .