Physics quiz question: charging capacitor

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

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

An ideal 15 V emf source connected to an ideal 70 kiloohm resistor and a 12 µF capacitor. The switch is closed at t = 0. At what time t will the voltage across the capacitor be 10 V?
(A) 0.28 s.
(B) 0.34 s.
(C) 0.56 s.
(D) 0.92 s.

Correct answer: (D)

For a charging capacitor, the potential difference across the capacitor as a function of time is given by:

delta(V) = emf*(1 - exp(-t/(R*C)),

such that solving for t:

t = -R*C*ln(1 - emf/delta(V)),

where the quantity inside the natural logarithm is (1 - emf/delta(V)) = (1 - (10 V)/(15 V)) = 1/3, thus:

t = –R*C*ln(1/3) = -(70e3 ohms)*(12e-6 F)*ln(1/3) = 0.922834322 s = 0.92 s.

Response (A) is (1/3)*R*C; response (B) is -R*C*ln(2/3); and response (C) is (2/3)*R*C.

Student responses
Section 31988
(A) : 0 students
(B) : 4 students
(C) : 6 students
(D) : 0 students

Success level: 0%
Discrimination index (Aubrecht & Aubrecht, 1983): 0