Q. The capacity of a parallel plate condenser is $10\mu F$ without dielectric. Dielectric of constant 2 is used to fill half the distance between the plates, the new capacitance in $\mu F$ is

A) 10
B) 20
C) 15
D) 13.33
Explanation

(d) $C = \frac{A\varepsilon_{0}}{d} = 10\mu F$
$C_{1} = \frac{A\varepsilon_{0}}{d - t + \frac{t}{k}} = \frac{A\varepsilon_{0}}{d - \frac{d}{2} + \frac{d}{2k}} = \frac{A\varepsilon_{0}}{\frac{d}{2}\left( 1 + \frac{1}{2} \right)} = \frac{4}{3}.\frac{A\varepsilon_{0}}{d}$
$\therefore C_{1} = \frac{4}{3} \times 10 = 13.33\mu F$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.