AP Physics 1 Exam Question: Capacitance

A parallel plate capacitor has a plate area of 0.02 square meters and a plate separation of 0.005 meters. The capacitor is connected to a 12-volt battery. Find the capacitance of the capacitor.

(Assume the electric field between the plates is uniform and there is no fringing effect.)

Let's start by recalling the formula for capacitance:

C = ε₀ * (A / d)

where C is the capacitance, ε₀ is the permittivity of free space, A is the area of the plates, and d is the plate separation.

Given values:

• A = 0.02 m² (plate area)
• d = 0.005 m (plate separation)
• ε₀ = 8.85 x 10⁻¹² F/m (permittivity of free space)

Step 1: Substitute the given values into the formula for capacitance:

C = (8.85 x 10⁻¹² F/m) * (0.02 m² / 0.005 m)

Step 2: Simplify the expression:

C = 8.85 x 10⁻¹² F/m * 4 m

Step 3: Calculate the product:

C = 3.54 x 10⁻¹¹ F

Therefore, the capacitance of the capacitor is 3.54 x 10⁻¹¹ Farads (F).