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

Options

A. 9.8 mJ
B. 4.6 mJ
C. 3.2 mJ
D. 2.5 mJ

Answer

(a)

Explanation

Energy loss
`Delta U = 1/2(C_(1)C_(2)/C_(1) + C_(2))(V_(1) - V_(2))^(2)`
`1/2 4 xx 10^(-6) xx 6 xx 10^(-6)/4 xx 10^(-6 ) + 6 xx 10^(-6) (80 - 30 )^(2) = 3 xx 10^(-3) J`
Initial energy of `C_(1) = 4 mu F` is,
`E_(1) = 1/2 C_(1)V_(1)^(2) = 12.8 xx 10^(-3)J`
Energy lost by `C_(1) = 12.8 xx 10^(-3) = 9.8`mJ