A charged condenser is made to share its charge with an uncharged condenser of twice its capacitance. Find the sum of the energy of the two condensers?

Explanation

Let the capacitance of the charged condenser be C and let its charge be Q.
Before sharing of charge, energy of the charged condenser is,
`E_1= (Q^2)/(2C)`
The capacitance of the other condenser = 2C, since the charged condenser is made to share its charge with the second condenser, it is clear that the condenser are connected in parallel with each other.
Equivalent capacitance of them `= C+2C= 3C`
Energy of the combination ` = (1)/(2)*(Q^2)/(3C)= (1)/(3)*(1)/(2) (Q^2)/(C )= (1)/(2)E_1`.