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_(1) V_(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_(2) v_(2)^(2)`
`implies CV^(2) = (1)/(2) xx 2C xx V_(2)^(2)`
`implies v_(2)^(2) = (V^(2))/(4)`
`:. V_(2) = (V)/(2)`