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 μm. 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 μm
B. $l$ = 3 cm, b = 1 cm, d = 30 μm
C. $l$ = 6 cm, b = 5 cm, d = 3 μm
D. $l$ = 1 cm, b = 1 cm, d = 10 μm
E. $l$ = 5 cm, b = 2 cm, d = 1 μm
Choose the correct answer from the options given below :

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C and E only

A only

B and D only

C only

answer is A.

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Detailed Solution

$C = \frac{A \in_{0}}{d}$
A : plate area
d : distance between the plates.
Capacitance initial
$= \frac{ϵ_{0} ℓ b}{d} = ϵ_{0} units$
Option 'C' $\begin{aligned} ℓ = 6 cm \\ b = 5 cm \\ d = 3 cm \end{aligned}$
Capacitance $= 10 ϵ_{0} units$
$Option 'E' ℓ = 5 cm$
$\begin{aligned} b = 2 cm \\ d = 1 cm \end{aligned}$
$Capacitance = 10 ϵ_{0} units$
$∴ Ans is option (1)$