JEE Main · 2026 · 02 Apr 2026 · Shift 1 · Capacitance

A parallel plate air capacitor has a capacitance C. When it is half filled as show in figure with a dielectric constant

K = 5

, the percentage increase in the capacitance is ____.

Answer: (B)

Solution

The dielectric of constant

K = 5

fills the upper half of the gap over the full plate area, so the system is two capacitors in series, each of separation

d /2

. Their capacitances are

C_{1} = \frac{K ϵ _{0} A}{d /2} = 10 C

and

C_{2} = \frac{ϵ _{0} A}{d /2} = 2 C

, where

C = \frac{ϵ _{0} A}{d}

. In series,

C_{f} = \frac{C _{1} C _{2}}{C _{1} + C _{2}} = \frac{( 10 C ) ( 2 C )}{12 C} = \frac{5 C}{3}

. The percentage increase is

\frac{5 C /3 - C}{C} \times 100 = \frac{2}{3} \times 100 \approx 66.67%

. The percentage increase in capacitance is

66.67%

JEE Main · 2026 · 02 Apr 2026 · Shift 1 · Single correct option