Question

The capacitance of a parallel plate capacitor will get doubled if

• A. the area of each plate is doubled
• B. the area of each plate is halved
• C. the distance between the plates is doubled
• D. the distance between the plates is halved

Hint:

For a parallel plate capacitor: \[ C=\frac{\varepsilon_0 A}{d} \] Capacitance increases with larger plate area and decreases with larger separation between plates.

Answer 1

The Correct Option is A, D

Step 1: Recall the formula for capacitance.
The capacitance of a parallel plate capacitor is given by
\[ C=\frac{\varepsilon_0 A}{d} \] where
\[ A=\text{area of plates} \] and
\[ d=\text{distance between the plates}. \]

Step 2: Understand dependence on area.
Capacitance is directly proportional to the area of the plates.
\[ C\propto A \] Therefore, if the area is doubled, capacitance also becomes doubled.
\[ A\rightarrow 2A \] \[ C\rightarrow 2C \]
Hence, option (A) is correct.

Step 3: Analyze halving of area.
If the area becomes half, then capacitance also becomes half.
\[ A\rightarrow \frac{A}{2} \] \[ C\rightarrow \frac{C}{2} \] Thus, option (B) is incorrect.

Step 4: Understand dependence on separation.
Capacitance is inversely proportional to the distance between the plates.
\[ C\propto \frac{1}{d} \]

Step 5: Analyze doubling of distance.
If the distance between the plates is doubled, capacitance becomes half.
\[ d\rightarrow 2d \] \[ C\rightarrow \frac{C}{2} \] Therefore, option (C) is incorrect.

Step 6: Analyze halving of distance.
If the distance between the plates is halved, capacitance becomes double.
\[ d\rightarrow \frac{d}{2} \] \[ C\rightarrow 2C \] Hence, option (D) is correct.

Step 7: Final conclusion.
Therefore, the capacitance gets doubled when:
\[ \boxed{\text{Area is doubled}} \] and
\[ \boxed{\text{Distance is halved}} \] Hence, the correct answers are options (A) and (D).