Question:

Consider a parallel plate capacitor with plate area A = 4 cm² and plate separation d = 0.5 mm. The capacitor is connected to a battery of voltage V = 12 V. Determine the capacitance of the capacitor.

Answer:

The capacitance of a parallel plate capacitor is given by the formula:

C = ε₀ * (A/d)

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

Given: A = 4 cm² = 4 * 10⁻⁴ m² d = 0.5 mm = 0.5 * 10⁻³ m

Substituting the given values into the formula, we get:

C = ε₀ * (A/d) = ε₀ * (4 * 10⁻⁴ / 0.5 * 10⁻³ )

Now we need to determine the value of ε₀. The permittivity of free space is a constant with a value of 8.85 x 10⁻¹² F/m.

Substituting ε₀ = 8.85 x 10⁻¹² F/m, we can calculate the capacitance as follows:

C = 8.85 x 10⁻¹² F/m * (4 * 10⁻⁴ / 0.5 * 10⁻³ )

Simplifying the expression within the parentheses:

C = 8.85 x 10⁻¹² F/m * (4 * 10⁻⁴ / 0.5 * 10⁻³ ) = 8.85 x 10⁻¹² F/m * (0.08)

Finally, multiplying the two values:

C = 8.85 x 10⁻¹² F/m * 0.08 = 7.08 x 10⁻¹³ F.

Therefore, the capacitance of the parallel plate capacitor is 7.08 x 10⁻¹³ F.