If you double the plate area and distance between the plates, what happens to capacitance?

If you double the plate area and distance between the plates, what happens to capacitance?

• A. It stays the same
• B. It doubles
• C. It halves
• D. It quadruples

Answer: (A)

Capacitance of a parallel-plate capacitor scales with the ratio of area to separation: C = ε0 A / d (for air or vacuum). Doubling the plate area tends to double the capacitance, since more surface can store charge at the same voltage. Doubling the distance between the plates tends to halve the capacitance, because increasing separation weakens the electric field for a given charge, reducing storage per volt. Doing both changes at once gives a factor of 2 from the area and a factor of 1/2 from the distance, which cancel out. With the medium unchanged, the overall capacitance remains the same.

Capacitance of a parallel-plate capacitor scales with the ratio of area to separation: C = ε0 A / d (for air or vacuum). Doubling the plate area tends to double the capacitance, since more surface can store charge at the same voltage. Doubling the distance between the plates tends to halve the capacitance, because increasing separation weakens the electric field for a given charge, reducing storage per volt. Doing both changes at once gives a factor of 2 from the area and a factor of 1/2 from the distance, which cancel out. With the medium unchanged, the overall capacitance remains the same.