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

Initial energy of body of capacitance `4 muF` is
`U_(i) = (1)/(2) xx (4 xx 10^(-6))(80)^(2) = 0.0128 J`
Final potential on this body after connection is
`V = (4 xx 80 + 6 xx 30)/(4 + 6) = 50 V1`. So final energy on it
`U_(f) = (1)/(2) xx 4 xx 10^(-6) (50)^(2) = 0.005 J`
Energy lost by this body `= U_(i) - U_(f) = 7.8 mJ`