The capacitance of a parallel-plate capacitor with plate area A, separation d and vacuum between plates is?

The capacitance of a parallel-plate capacitor with plate area A, separation d and vacuum between plates is?

• A. C = ε0 A / d
• B. C = d/(ε0 A)
• C. C = ε0 d / A
• D. C = A / (ε0 d)

Answer: (A)

The ability of a parallel-plate capacitor to store charge depends on how much plate area is facing each other and how far apart the plates are. In vacuum, the relevant constant is ε0, so the capacitance scales with area and inversely with separation: more area means more charge can be stored for a given voltage, and larger separation makes it harder to store charge. Derivation sketch: between the plates the electric field is roughly uniform, with E = Q/(ε0 A). The potential difference is V = E d = Q d /(ε0 A). The capacitance is C = Q/V, which gives C = ε0 A / d. If a dielectric with relative permittivity εr were present, it would become C = ε0 εr A / d, but for vacuum εr = 1. So the correct relation is C = ε0 A / d. The other forms would either imply the wrong dependence on A or d (for example, increasing separation would wrongly appear to increase capacitance), or have inconsistent units, so they don’t match the physical relationship.

The ability of a parallel-plate capacitor to store charge depends on how much plate area is facing each other and how far apart the plates are. In vacuum, the relevant constant is ε0, so the capacitance scales with area and inversely with separation: more area means more charge can be stored for a given voltage, and larger separation makes it harder to store charge.

Derivation sketch: between the plates the electric field is roughly uniform, with E = Q/(ε0 A). The potential difference is V = E d = Q d /(ε0 A). The capacitance is C = Q/V, which gives C = ε0 A / d. If a dielectric with relative permittivity εr were present, it would become C = ε0 εr A / d, but for vacuum εr = 1.

So the correct relation is C = ε0 A / d. The other forms would either imply the wrong dependence on A or d (for example, increasing separation would wrongly appear to increase capacitance), or have inconsistent units, so they don’t match the physical relationship.