Physics quiz question: different gap capacitors

Physics 205B Quiz 4, Fall Semester 2010
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 17.55

Two parallel plate capacitors have the same area, and same charge, but different separation gaps. The parallel plate capacitor with the ___________ separation gap has a greater potential difference.
(A) wider.
(B) narrower.
(C) (There is a tie.)
(D) (Not enough information is given.)

Correct answer: (A)

Both capacitors have the same area, but different separation gaps. The wider separation gap capacitor will have the smaller capacitance, as seen from:

C = A/(4*pi*k*d).

Both capacitors have the same charge. So the wider separation gap capacitor, having the smaller capacitance, will have the greater potential difference as seen from:

delta(V) = Q/C = Q/(A/(4*pi*k*d)) = 4*pi*k*Q*d/A = (4*pi*k*Q/A)*d.

Student responses
Section 70856
(A) : 8 students
(B) : 3 students
(C) : 0 students
(D) : 0 students

Success level: 72%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.50