Question Detail
Question
In a parallel-plate capacitor, the distance d between the plates is 3cm, the area of each plate is 15cm2, and the voltage across them is 5V. Calculate the capacitance. Take permittivity of free space to be ε0 = 8.854 × 10-12 C2/Nm2.
Correct Answer
Option C is the correct answer.
Detailed Explanation
The capacitance (C) of a parallel-plate capacitor is given by the formula:C = ε0 * A / dWhere: ε0 = 8.854 × 10-12 C2/Nm2 (permittivity of free space)A = 15 cm2 = 15 × (10-2 m)2 = 15 × 10-4 m2d = 3 cm = 3 × 10-2 mC = (8.854 × 10-12 C2/Nm2) * (15 × 10-4 m2) / (3 × 10-2 m)C = (8.854 × 10-12 * 15 / 3) × 10-4 / 10-2 FC = (8.854 × 10-12 * 5) × 10-2 FC = 44.27 × 10-14 FC = 4.427 × 10-13 FThe closest option is 4.43 × 10-13 F.
Hint
Convert all units to SI (meters) before applying the formula C = ε0A/d.