Doubling the distance between plates of a parallel-plate capacitor, while keeping plate area and dielectric the same, will cause the capacitance to

• A. Double.
• B. Increase by a factor of four.
• C. Halve.
• D. Stay the same.

Answer: (C)

Doubling the separation between the plates reduces the capacitance because, for a parallel-plate capacitor with fixed area and dielectric, capacitance scales as C = ε A / d. If you replace the distance d with 2d, you get C = ε A / (2d) = (1/2) (ε A / d). So the capacitance becomes half of its original value.

Intuitively, increasing the gap makes it harder to store charge for a given voltage, since the electric field lines spread out over a larger distance. Using Q = C V, for the same charge Q, doubling the distance would require a larger voltage V, meaning the same device stores less charge per unit voltage.