A body of capacity `4 muF` is charged to `80V` and another body of capacity `6muF` is charged to `30V`. When they are connected the energy lost by `4 muF` capacitor is

Options

A. 7.8 mJ
B. 4.6 mJ
C. 3.2 mJ
D. 2.5 mJ

Answer

A

Explanation

Common potential, `V = (C_(1)V_(1) + C_(2)V_(2))/(C_(1) + C_(2))`
`= ((4 xx 10^(-6)) xx 80 + (6 xx 10^(-6)) xx 30)/(4 xx 10^(-6) + 6 xx 10^(-6))`
`:.` Energy lost by `4 mu F` capacitor is
`= (1)/(2)C_(1)V_(1)^(2) - (1)/(2)C_(1)V^(2) = (1)/(2)C_(1)(V_(1)^(2) - V^(2))`
`= (1)/(2) xx (4 xx 10^(-6)) xx {(80)^(2) - (50)^(2)} = 7.8 xx 10^(-3) J = 7.8 J`