Question Detail

PHY 102 Test Compilation PHY 102 17 Objective Question

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 x 10-12 C²/Nm².
Options
A 3.33 x 10<sup>-13</sup> F
B 9.31 x 10<sup>-11</sup> F
C 4.43 x 10<sup>-13</sup> F
Correct Answer
D 1.29 x 10<sup>-11</sup> F
Correct Answer

Option C is the correct answer.

Detailed Explanation

The capacitance (C) of a parallel-plate capacitor is given by C = ε₀A/d, where ε₀ is the permittivity of free space, A is the area of the plates, and d is the distance between the plates. Given: A = 15 cm² = 15 x 10-4 m², d = 3 cm = 3 x 10-2 m, ε₀ = 8.854 x 10-12 F/m. C = (8.854 x 10-12 F/m) * (15 x 10-4 m²) / (3 x 10-2 m) = (8.854 * 15 / 3) x 10-12-4+2 F = (8.854 * 5) x 10-14 F = 44.27 x 10-14 F = 4.427 x 10-13 F. This rounds to 4.43 x 10-13 F.

Hint

The formula for capacitance of a parallel plate capacitor is C = ε₀A/d. Ensure all units are in SI before calculation.

Question Info