Physics quiz question: greater potential difference capacitor

Physics 205B Quiz 4, spring semester 2013
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Comprehensive Problem 17.79(b)

Two parallel plate capacitors have different areas, different separation gaps, but the same amount of electric potential energy. The parallel plate capacitor with the ___________ has a greater potential difference.
(A) smaller area and larger separation gap.
(B) larger area and smaller separation gap.
(C) (There is a tie.)
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (A)

Both capacitors have the same electric potential energy:

EPE = (1/2)·Q·ΔV = (1/2)·C·(ΔV)² = Q²/(2·C).

However, the capacitor with the smaller area A and the larger separation gap d would have the lower capacitance, as seen from:

C = A/(4·π·k·d).

Thus from EPE = (1/2)·C·(ΔV)², the capacitor with the lower capacitance C would have the greater potential difference ΔV.

Section 30882
Exam code: quiz04eQu7
(A) : 9 students
(B) : 16 students
(C) : 8 students
(D) : 1 student

Success level: 24%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.28