Physics quiz question: decreasing voltage applied to capacitor

Physics 205B Quiz 4, Spring Semester 2011
Cuesta College, San Luis Obispo, CA

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

Consider a Power Acoustik™ PCX-5F sound system capacitor*, with a capacitance of 5.0 F, connected to a 24 V battery. If the voltage of the capacitor is decreased from 24 V to 12 V, the capacitance will:
(A) decrease.
(B) remain the same.
(C) increase.
(D) (Not enough information is given.)

*http://www.sonicelectronix.com/item_12013_Power-Acoustik-PCX-5F.html.

Correct answer: (B)

The capacitance of a parallel-plate capacitor depends on its construction (surface area, separation gap, etc.) and not on how much voltage difference is applied to it, nor how much charge is stored in it:

C [proportional to] Area/distance.

Since neither area nor distance is changed, then reducing the voltage applied to the capacitor will not change its capacitance, but it will decrease the charge stored in it:

C = Q/delta(V),

where again C must remain constant as both delta(V) and Q decrease.

Student responses
Section 30822
Exam code: quiz04t4c0
(A) : 0 students
(B) : 2 students
(C) : 6 students
(D) : 0 students

Success level: 25%
Discrimination index (Aubrecht & Aubrecht, 1983): -0.50