Chapter 25 Problem 54 † Given t = 5.0 ms Solution a) Find the time

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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
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