A capacitor of capacity `C` is charged to a potential difference `V` and another capacitor of capacity `2C` is charged to a potential difference `4V`. The charged batteries are disconnected and the two capacitors are connected with reverse polarity (i.e. positive plate of first capacitor is connected to negative plate of second capacitor). The heat produced during the redistribution of charge between the capacitors will be

Options

A. `(125CV^2)/3`
B. `(50CV^2)/3`
C. `2CV^2`
D. `(25CV^2)/3`

Answer

D

Explanation

Total charge=`(2C)(4V)-CV`
`=7CV`
`V_C=("Total charge")/("Total capacitance")`
`(7CV)/(2C+C)=7/3V`
Heat `=U_i+U_f`
`=1/2CV^2+1/2(2C)(4V)^2-1/2xx3Cxx(7/3V)^2`
`=25/3CV^2`