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 B. l=3 cm , b =1 cm , d =30 μ m C. l=6 cm , b =5 cm , d =3 μ m D. l=1 cm , b =1 cm , d =10 μ m E. l=5 cm , b =2 cm , d =1 μ m

Physics · Capacitors and R-C Circuits

JEE Main 2025 — 24 January, Morning Shift — Question 64

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

$l=3 \mathrm{~cm}$ and breath of $\mathrm{b}=1 \mathrm{~cm}$ . 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. $l=5 \mathrm{~cm}, \mathrm{~b}=2 \mathrm{~cm}, \mathrm{~d}=1 \mu \mathrm{~m}$

$C=\frac{A \epsilon_{0}}{d}$

A : plate area

d : distance between the plates.

Capacitance initial

$=\frac{\epsilon_{0} \ell b}{d}=\epsilon_{0}$ units

Option ' $\mathrm{C}^{\prime} \quad \ell=6 \mathrm{~cm}$

$\mathrm{b}=5 \mathrm{~cm}$

$\mathrm{~d}=3 \mathrm{~cm}$

Capacitance $=10 \epsilon_{0}$ units

Option 'E' $\quad \ell=5 \mathrm{~cm}$

$\mathrm{b}=2 \mathrm{~cm}$

$\mathrm{~d}=1 \mathrm{~cm}$

Capacitance $=10 \epsilon_{0}$ units

$\therefore$ Ans is option (1)

Answer key and solution verified before publishing.

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