A parallel plate capacitor was made with two rectangular plates, … - Vidyadip

MCQ

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 :

✓
C and E only
B
B and D only
C
A only
D
C only

✓

Answer

Correct option: A.

C and E only

(A)
Sol. $\mathrm{C}=\frac{\mathrm{A} \in_{0}}{\mathrm{~d}}$
A : plate area
d : distance between the plates.
Capacitance initial
$=\frac{\in_{0} \ell \mathbf{b}}{d}=\in_{0}$ units
Option ' C ' $\quad \ell=6 \mathrm{~cm}$
$
\begin{aligned}
& \mathrm{b}=5 \mathrm{~cm} \\
& \mathrm{~d}=3 \mathrm{~cm}
\end{aligned}
$
Capacitance $=10 \in_{0}$ units
Option 'E' $\quad \ell=5 \mathrm{~cm}$
$
\begin{aligned}
& \mathrm{b}=2 \mathrm{~cm} \\
& \mathrm{~d}=1 \mathrm{~cm}
\end{aligned}
$
Capacitance $=10 \in_{0}$ units
$\therefore$

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