Q. What will be the capacity of a parallel-plate capacitor when the half of parallel space between the plates is filled by a material of dielectric constant $\varepsilon_{r}?$ Assume that the capacity of the capacitor in air is $C$
A) $\frac{2\varepsilon_{r}C}{1 + \varepsilon_{r}}$
B) $\frac{C(\varepsilon_{r} + 1)}{2}$
C) $\frac{C\varepsilon_{r}}{1 + \varepsilon_{r}}$
D) $\varepsilon_{r}C$
Explanation
(a) $C = \frac{\varepsilon_{0}A}{d}$
$C_{N} = \frac{C_{1}C_{2}}{C_{1} + C_{2}} = \frac{\frac{\varepsilon_{0}A}{d/2}.\frac{\varepsilon_{0}\varepsilon_{r}A}{d/2}}{\frac{\varepsilon_{0}A}{d/2} + \frac{\varepsilon_{0}\varepsilon_{r}A}{d/2}}$
$= \frac{2\varepsilon_{0}A\varepsilon_{r}}{d\left( 1 + \varepsilon_{r} \right)} = \frac{2C\varepsilon_{r}}{(1 + \varepsilon_{r})}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.