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Chapter 25 Problem 54 † Given t = 5.0 ms Solution a) Find the time to reach 1 − 1/e3 of the battery voltage. The model for voltage across a charging capacitor is V = V0 1 − e−t/RC When t = RC, one time constant has transpired and V = V0 1 − e−1 = V0 (1 − 1/e) In three time constants, t = 3RC and V = V0 1 − e−3 = V0 1 − 1/e3 Since this is the condition mentioned in the problem, the time to reach 1 − 1/e3 of the battery voltage is t = 3(5.0 ms) = 15 ms b) Find the capacitance if R = 22 kΩ. Since a time constant is τ = RC Then capacitance is τ 1.0 × 10−3 s C= = 4.55 × 10−6 F = 4.55 µF = 3 R 22 × 10 Ω † Problem from Essential University Physics, Wolfson