A parallel plate capacitor was made with two rectangular plates, each with a length of $l=3 \mathrm{~cm}$ and breath of $b=1 \mathrm{~cm}$. The distance between the plates is $3 \mu \mathrm{~m}$. Out of the following, which are the ways to increase the capacitance by a factor of 10 ? A. $l=30 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=1 \mu \mathrm{~m}$ B. $l=3 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=30 \mu \mathrm{~m}$ C. $l=6 \mathrm{~cm}, \mathrm{~b}=5 \mathrm{~cm}, \mathrm{~d}=3 \mu \mathrm{~m}$ D. $l=1 \mathrm{~cm}, \mathrm{~b}=1 \mathrm{~cm}, \mathrm{~d}=10 \mu \mathrm{~m}$ E. $l=5 \mathrm{~cm}, \mathrm{~b}=2 \mathrm{~cm}, \mathrm{~d}=1 \mu \mathrm{~m}$ Choose the correct answer from the options given below :

JEE Main · 2025 · 24 Jan 2025 · Shift 1 · Capacitance

A parallel plate capacitor was made with two rectangular plates, each with a length of

l = 3 cm

and breath of

b = 1 cm

. The distance between the plates is

3 μ m

. Out of the following, which are the ways to increase the capacitance by a factor of 10 ?
A.

l = 30 cm, b = 1 cm, d = 1 μ m

l = 3 cm, b = 1 cm, d = 30 μ m

l = 6 cm, b = 5 cm, d = 3 μ m

l = 1 cm, b = 1 cm, d = 10 μ m

l = 5 cm, b = 2 cm, d = 1 μ m

Choose the correct answer from the options given below :

Answer: (A)

Capacitance of a parallel plate capacitor is

C = \frac{ε _{0} l b}{d}

.

Original:

l = 3

cm,

b = 1

cm,

d = 3 μ m

, giving

C_{0} = ε_{0} \frac{3 \times 1}{3} = ε_{0}

in these units.

For the capacitance to become

10 C_{0}

, check each option using

C = ε_{0} \frac{l b}{d}

:

A:

\frac{30 \times 1}{1} = 30 ε_{0}

— no

B:

\frac{3 \times 1}{30} = 0.1 ε_{0}

— no

C:

\frac{6 \times 5}{3} = 10 ε_{0}

— yes

D:

\frac{1 \times 1}{10} = 0.1 ε_{0}

— no

E:

\frac{5 \times 2}{1} = 10 ε_{0}

— yes

Options C and E give exactly a tenfold increase in capacitance.

JEE Main · 2025 · 24 Jan 2025 · Shift 1 · Single correct option