A capacitor C is charged by a battery with internal resistance R. At what time does the potential difference across the resistor become n times that across the capacitor?
Options

Question

A capacitor C is charged by a battery with internal resistance R. At what time does the potential difference across the resistor become n times that across the capacitor?

G1 Physics · Accepted Answer

During charging, Vᵣ=E exp(−t/RC) and V꜀=E(1−exp(−t/RC)). Set Vᵣ=nV꜀. Then exp(−t/RC)=n/(1+n), so t=RC ln[(1+n)/n]. Correct answer: A.