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The capacitance of a parallel-plate condenser is $10\,\mu\text{F}$ when the distance between its plates is 8 cm. If the distance between the plates is reduced to 4 cm, then the capacitance will be

1. $5\,\mu\text{F}$
2. $10\,\mu\text{F}$
3. $20\,\mu\text{F}$
4. $40\,\mu\text{F}$

Correct answer: $20\,\mu\text{F}$

Solution

For a parallel-plate capacitor, $C\propto \frac{1}{d}$. When the separation is reduced from 8 cm to 4 cm, the distance is halved, so the capacitance doubles from $10\,\mu\text{F}$ to $20\,\mu\text{F}$.

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