Question

A capacitor of capcitance $C$ 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. Depends on the value of the resistance

Answer 1

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


Given,

Initial charge on the capacitor is $Q$.

$\therefore$ Initial energy of the system,

$U_i=\frac{Q^2}{2C}$

As another identical uncharged capacitor is connected with the given charged capacitor. Thus, each of them finally have charge $\frac{Q}{2}$

$\therefore$ Final energy of the system,

$U_f=2\left[\frac{{\left(\frac{Q}{2}\right)}^2}{2C}\right]=\frac{Q^2}{4C}$

Now,
$\text{Heat produced=loss in eneregy=}{U}_i-U_f=\frac{Q^2}{4C}$

Hence, option $\left(b\right)$ is correct.