JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Capacitance

A capacitor has capacitance

5 μ F

when it's parallel plates are separated by air medium of thickness d . A slab of material of dielectric constant 1.5 having area equal to that of plates but thickness

\frac{d}{2}

is inserted between the plates. Capacitance of the capacitor in the presence of slab will be

____

μ F

Answer: 6

Solution

The empty capacitor has

C_{0} = \frac{ϵ _{0} A}{d} = 5 μ F

. Filling half the gap leaves two capacitors in series: an air layer of thickness

d /2

with

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

, and a dielectric layer of thickness

d /2

with

C_{2} = \frac{1.5 ϵ _{0} A}{d /2} = 3 C_{0}

. Combining them,

\frac{1}{C} = \frac{1}{2 C _{0}} + \frac{1}{3 C _{0}} = \frac{5}{6 C _{0}}

, so

C = \frac{6}{5} C_{0} = \frac{6}{5} \times 5 = 6 μ F

JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Integer answer

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