Question

A parallel plate condenser with plate separation d is charged with the help of a battery so that $U_0$ energy is stored in the system. A plate of dielectric constant k and thickness d is placed between the plates of condenser while battery remains connected . The new energy of the system will be

• A. $K{U}_0$
• B. $K^2{U}_0$
• C. $\frac{U_0}{K}$
• D. $\frac{U_0}{K^2}$

Answer 1

The correct option is C $\frac{U_0}{K}$

After inserting the dielectric materials $\left(K\right)$

Capacitance $C^{\prime }=KC$

Potential difference $V^{\prime }=\frac{V}{K}$

Energy stored $=\frac{1}{2}C{V}^2$

$=\frac{1}{2}\times KC{\left(\frac{V}{K}\right)}^2$

$=\frac{1}{2}\times \frac{C{V}^2}{K}=\frac{U_A}{K}$