Physics quiz question: discharging capacitor

Physics 205B Quiz 5, Fall Semester 2010
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 18.83

Consider a 20 µF capacitor connected to an 8.0 kV potential difference such that it is fully charged. The capacitor is then disconnected from the potential source, and a 200 ohm resistor is connected to the capacitor at t = 0. At what time t will the voltage across the capacitor have 50% of its original value?
(A) 0.0020 s.
(B) 0.0028 s.
(C) 0.11 s.
(D) 0.69 s.

Correct answer: (B)

For a discharging capacitor,

delta(V) = emf*exp(-t/tau),

where the time constant tau = R*C. Solving for t:

delta(V)/emf = exp(-t/tau),

ln(delta(V)/emf) = -t/tau,

t = -tau*ln(delta(V)/emf) = -R*C*ln(delta(V)/emf) = -(200 ohms)*(20e-6 farads)*ln(0.50) = 0.002772588722 s ≈ 0.0028 s.

Response (A) is R*C/2; response (C) is -C*emf*ln(1/2); response (D) is -ln(1/2).

Student responses
Section 70856
(A) : 1 student
(B) : 7 students
(C) : 2 students
(D) : 1 student

Success level: 63%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.83