Question

A potential difference of $\Delta V$exists between two plates of a parallel-plate capacitor with capacitance C . A dielectric with a dielectric constant of k is then placed between the plates of the capacitor. What is the energy stored in the capacitor?

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

Answer 1

The correct option is C $\frac{1}{2}kC(\Delta V{)}^2$

When the dielectric is inserted in between plates, the capacitance of the capacitor becomes $C^{\prime }=KC$

Thus, now the energy stored, $U^{\prime }=\frac{1}{2}{C}^{\prime }{V}^2=\frac{1}{2}\left(KC\right)(\Delta V{)}^2$