Question

A dielectric with a dielectric constant of $k$ is inserted between the plates of the capacitor of capacitance $C$ having a potential difference of $\Delta V$ between the two plates. Calculate the energy stored in the capacitor?

• A. $\frac{1}{2}\left(C/k\right){\left(\Delta V\right)}^2$
• B. $\frac{1}{2}\left(k/C\right){\left(\Delta V\right)}^2$
• C. $\frac{1}{2}kC{\left(\Delta V\right)}^2$
• D. $\frac{1}{2}kC\Delta V$
• E. $\frac{1}{2}\left(C/k\right)\Delta V$

Answer 1

Answer: (C)

$\frac{1}{2}kC{\left(\Delta V\right)}^2$

The energy stored in a air (or vacuum between plates) filled capacitor is given by

$E=\frac{1}{2}C\Delta V^2$

when dielectric $k$ is filled between the plates ,the energy stored will be ,

$E^{\prime }=\frac{1}{2}{C}^{\prime }\Delta V^2$

since , $k=C^{\prime }/C$

therefore , $E^{\prime }=\frac{1}{2}kC\Delta V^2$