A larallel plate capacitor was made with two rectangular plates, each with a length of = 3 cm and breath of b = 1 cm. The distance between the plates is 3 m. Out of the following, which are the ways to increase the capacitance by a factor of 10? A. = 3

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Solution

Q.
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

Choose the correct answer from the options given below: [2025]

1 C and E only

2 B and D only

3 A only

4 C only

Ans.
(1)

We know $C = \frac{A ε_{0}}{d} = \frac{b l ε_{0}}{d}$

So, to increase the capacitance by factor $10 (\frac{A}{d})$ has to increase by factor 10.

For option (A) $C' = 30 C$

For option (B) $C' = \frac{C}{10}$

For option (C) $C' = 10 C$

For option (D) $C' = \frac{C}{10}$

For option (E) $C' = 10 C$

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