Physics quiz question: charging capacitors

Physics 205B Quiz 5, spring semester 2012
Cuesta College, San Luis Obispo, CA

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

A resistor and an uncharged capacitor are connected either to a 12 V ideal emf, or a 6.0 V ideal emf. After the switches are closed at t = 0, the capacitor attached to the __________ will take a longer time to reach 95% of its final value.
(A) 12 V ideal emf.
(B) 6.0 V ideal emf.
(C) (There is a tie.)
(D) (Not enough information is given.)

Correct answer: (C)

The voltage across a charging capacitor as a function of time is given by;

ΔV(t) = ε*(1 - exp(-t/τ).

Since both circuits have the same resistance R and capacitance C, they will have the same time constant τ = R*C, and have the same relative time dependence, reaching 95% of their respective final ε values in the same time.

Section 30882
Exam code: quiz05Vo7x
(A) : 10 students
(B) : 7 students
(C) : 9 students
(D) : 0 students

Success level: 35%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.24

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