1. Concept: Capacitance scales with plate area and is inversely proportional to plate separation. The area of rectangular plates is Length \( \times \) Width.
2. Formula: $$ C = \frac{\epsilon_0 A}{d} = \frac{\epsilon_0 (L \times W)}{d} $$
3. Solution: - If length \( L \) and width \( W \) are doubled, the new area becomes \( A' = (2L) \times (2W) = 4(LW) = 4A \).
- The separation \( d \) is also doubled, so \( d' = 2d \).
- Substitute these into the formula: \( C' = \frac{\epsilon_0 (4A)}{2d} = 2 \left(\frac{\epsilon_0 A}{d}\right) = 2C \).
- The net result is a doubled capacitance.
4. Why other options are incorrect: Option C assumes only area changed. Option D incorrectly multiplies the factors instead of balancing the numerator and denominator.
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