Physics quiz question: different charge capacitors

Physics 205B Quiz 4, spring semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Conceptual Question 17.15

Two parallel plate capacitors have the same area, and same separation gaps, but different amounts of charge. The parallel plate capacitor with the ___________ amount of charge has a greater capacitance.
(A) lesser.
(B) greater.
(C) (There is a tie.)
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (C)

Both capacitors have the same area A and the same separation gap d, thus they must have the same capacitance, as seen from:

C = A/(4·π·k·d).

(However, these capacitors have different amounts of charge Q. So the capacitor with the greater amount of charge will have the greater potential difference as seen from:

ΔV = Q/C.)

Section 30882
Exam code: quiz04j0uL
(A) : 0 students
(B) : 13 students
(C) : 13 students
(D) : 0 students

Success level: 50%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.35