The capacitance of a parallel plate capacitor is 20 μf in air and 60 μf in the presence of a dielectric. What is the dielectric constant?

Analyze the question You are given the capacitance of a parallel plate capacitor in air (C₀ = 20 μF) and with a dielectric between the plates (C = 60 μF). You need the dielectric constant (relative permittivity, εᵣ).

Concept The dielectric constant is the factor by which the capacitance increases when a dielectric replaces air (or vacuum) between the plates:

εᵣ = C with dielectric / C in air

Solution

εᵣ = 60 μF / 20 μF = 3.0

The units cancel, so the dielectric constant has no unit.

Answer The dielectric constant is 3.0, which is option C.

Why the other options are wrong

• A (0.3) comes from inverting the ratio (20/60 is about 0.33). A dielectric always increases capacitance, so εᵣ must be greater than 1.
• B (6.0) and D (2.0) do not come from any correct use of the numbers.

Tip Remember "with over without": εᵣ = C(with dielectric) ÷ C(air). If your answer is below 1, you have flipped the ratio, since the dielectric constant of any material is at least 1.