Question

A capacitor of capacitance $C$ has charge $Q$. It is connected to an identical capacitor through a resistance. The heat produced in the resistance is

• A. $\frac{Q^2}{2C}$
• B. $\frac{Q^2}{4C}$
• C. $\frac{Q^2}{8C}$
• D. $Dependentonthevalueoftheresistance$

Answer 1

The correct option is B $\frac{Q^2}{4C}$

Initial energy of the system is $U=\frac{Q^2}{2C}$.
When connect a identical with the first one, the final charge on each capacitor is $Q/2$ because total charge is conserved.
Now the final energy of the system is $U_f=\frac{(Q/2{)}^2}{2C}+\frac{(Q/2{)}^2}{2C}=\frac{Q^2}{4C}$
$\therefore$ Heat produced $=$ loss in energy $=U_i-U_f=\frac{Q^2}{2C}-\frac{Q^2}{4C}=\frac{Q^2}{4C}$