Question

A parallel plate capacitor was made with two rectangular plates, each with a length of \( l = 3 \, {cm} \) and breadth of \( b = 1 \, {cm} \). The distance between the plates is \( d = 3 \, \mu{m} \). Out of the following, which are the ways to increase the capacitance by a factor of 10?

• A. C and E only
• B. B and D only
• C. A only
• D. C only

Hint:

In a parallel plate capacitor, the capacitance is proportional to the area of the plates and inversely proportional to the distance between them. To increase the capacitance by a factor of 10, ensure the product of the length and breadth increases while adjusting the distance accordingly.

Answer 1

The Correct Option is A

For a parallel plate capacitor, the capacitance is given by: \[ C = \varepsilon_0 \frac{l \times b}{d} \] The capacitance will increase by a factor of 10 if the following condition is met: \[ \frac{l_{\text{new}} \times b_{\text{new}}}{d_{\text{new}}} = 10 \] Evaluating the options: - Option A does not satisfy the condition.
- Option B does not satisfy the condition.
- Option C satisfies the condition because:
\[ \frac{6 \times 5}{3} = 10 \] - Option D does not satisfy the condition.
- Option E satisfies the condition because:
\[ \frac{5 \times 2}{1} = 10 \] Thus, the correct answer is \( \boxed{C \text{ and } E} \).