AP Physics 2 Exam: Capacitance

Question:

A parallel plate capacitor is filled with a dielectric material that has a relative permittivity of 3. If the distance between the plates is 0.02 meters, and the area of each plate is 0.1 square meters, calculate the capacitance of the capacitor.

Answer:

Step 1: Given data Relative permittivity of dielectric material (εᵣ) = 3 Distance between the plates (d) = 0.02 meters Area of each plate (A) = 0.1 square meters

Step 2: Formula for Capacitance The capacitance (C) of a parallel plate capacitor is given by the formula:

C = (ε₀ * εᵣ * A) / d

where ε₀ is the permittivity of free space (ε₀ ≈ 8.85 × 10⁻¹² F/m).

Step 3: Calculations Substituting the given values into the formula, we have:

C = (8.85 × 10⁻¹² F/m * 3 * 0.1 square meters) / 0.02 meters

C = (8.85 × 10⁻¹² F/m * 3 * 0.1) / 0.02

C = (2.655 × 10⁻¹²) / 0.02

C = 1.3275 × 10⁻¹¹ F

Step 4: Final Answer The capacitance of the parallel plate capacitor is approximately 1.3275 × 10⁻¹¹ Farads (F).

Therefore, the capacitance of the capacitor is 1.3275 × 10⁻¹¹ F.