JEE Main · 2023 · 25 Jan 2023 · Shift 1 · Capacitance

A parallel plate capacitor has plate area

40 cm^{2}

and plates separation 2 mm. The space between the plates is filled with a dielectric medium of a thickness 1 mm and dielectric constant 5. The capacitance of the system is:

(A) $24 ε_{0} F$
(B) $\frac{3}{10} ε_{0} F$
(C) $\frac{10}{3} ε_{0} F$ ✓ Correct
(D) $10 ε_{0} F$

Answer: (C)

Solution

A slab filling part of the gap acts as two capacitors in series, one of thickness

t = 1 mm

with constant

K = 5

and one of air of thickness

d - t = 1 mm

, so

\frac{1}{C} = \frac{t}{K ε _{0} A} + \frac{d - t}{ε _{0} A}

. With

A = 40 \times 1 0^{- 4} m^{2}

the two terms are

\frac{1}{20 ε _{0}}

and

\frac{1}{4 ε _{0}}

, summing to

\frac{6}{20 ε _{0}} = \frac{3}{10 ε _{0}}

. The capacitance of the system is

C = \frac{10}{3} ε_{0} F

JEE Main · 2023 · 25 Jan 2023 · Shift 1 · Single correct option

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