Question:

A parallel plate capacitor has square plates with side length 0.2 meters and is separated by a distance of 0.01 meters. The space between the plates is filled with a dielectric material of relative permittivity 4.0. If a potential difference of 100 volts is applied across the plates, what is the capacitance of the capacitor?

(A) 1.0 x 10^-6 F (B) 4.0 x 10^-12 F (C) 1.0 x 10^-10 F (D) 2.0 x 10^-12 F

Answer:

The capacitance of a parallel plate capacitor with a dielectric material can be calculated using the formula:

C = (k * ε₀ * A) / d

Where: C = capacitance k = relative permittivity of the dielectric ε₀ = permittivity of free space (8.85 x 10^-12 F/m) A = area of the plates d = distance between the plates

First, let's calculate the area of the plates: A = side length * side length A = 0.2 m * 0.2 m A = 0.04 m²

Now, we can calculate the capacitance using the given values: C = (4.0 * 8.85 x 10^-12 F/m * 0.04 m²) / 0.01 m C = (4.0 * 8.85 x 10^-12 F/m * 0.04 m²) / 0.01 m C = 1.416 x 10^-11 F

So, the capacitance of the capacitor is approximately 1.416 x 10^-11 F, which is closest to option (C).

Therefore, the correct answer is:

(C) 1.0 x 10^-10 F