Question Detail
Question
In a parallel-plate capacitor, the distance d between the plates is 3 cm, the area of each plate is 15 cm2, and the voltage across them is 5V. Calculate the capacitance. Take permittivity of free space to be ε0 = 8.854 x 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 = ε0A/d, where ε0 is the permittivity of free space, A is the area of the plates, and d is the distance between them.Given:A = 15 cm2 = 15 x 10-4 m2d = 3 cm = 3 x 10-2 mε0 = 8.854 x 10-12 C2/Nm2C = (8.854 x 10-12 C2/Nm2) * (15 x 10-4 m2) / (3 x 10-2 m)C = (8.854 * 15 / 3) * 10(-12 - 4 + 2) FC = (8.854 * 5) * 10-14 FC = 44.27 x 10-14 F = 4.427 x 10-13 F.Rounding to two decimal places, C ≈ 4.43 x 10-13 F.
Hint
Ensure all units are converted to SI units (meters, Farads) before calculation. The voltage (5V) is not needed for calculating capacitance.