How does the dielectric constant κ affect the capacitance for a capacitor with fixed geometry?

How does the dielectric constant κ affect the capacitance for a capacitor with fixed geometry?

• A. C increases proportionally to κ
• B. C decreases with κ
• C. C is independent of κ
• D. C increases with 1/κ

Answer: (A)

Capacitance with a dielectric scales with the dielectric constant κ. For a parallel-plate capacitor, the formula is C = κ ε0 A / d. With fixed geometry, A and d don’t change, and ε0 is a constant, so C grows directly in proportion to κ.

Physically, inserting a dielectric lowers the electric field for a given charge, which means the voltage across the plates becomes smaller (V = Q/C). Since the same charge then corresponds to a larger capacitance, C increases as κ increases. This linear relationship is why the correct view is that capacitance increases proportionally with κ. The ideas that it’s independent of κ or that it increases with 1/κ don’t match the basic formula or the underlying physics.