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 capacitance law.
\[ C = \frac{\varepsilon_0 A}{d} \] so $C$ grows with plate area and shrinks with plate spacing.

Step 2: Double the area.
If $A$ becomes $2A$, then $C$ doubles. So that option works.

Step 3: Halve the area.
If $A$ becomes $A/2$, then $C$ is cut in half, which is not what we want.

Step 4: Change the spacing.
Doubling $d$ halves $C$, but halving $d$ doubles $C$. So shrinking the gap to half also doubles the capacitance.

Step 5: Answer.
Area doubled and distance halved both work. \[ \boxed{A,\ D} \]