Q. An air filled parallel plate capacitor has a capacity of 2pF. The separation of the plates is doubled and the interspace between the plates is filled with wax. If the capacity is increased to 6 pF, the dielectric constant of wax is
A) 2
B) 3
C) 4
D) 6
Explanation
(d) Capacitance with air
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ C = \frac{A\varepsilon_{0}}{d}$
When interspace between the plates is filled with wax, then
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ C^{'} = \ \frac{KA\varepsilon_{0}}{2d}$
or $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ C^{'} = \left( \frac{A\varepsilon_{0}}{d} \right)\frac{K}{2}\ $
or $C^{'} = \ C\frac{K}{2}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 6 = 2.\frac{K}{2}\ \Rightarrow K = 6$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.