Saturday, May 24, 2008
MP8-2: Problem 31.72
On page 986 of the text, you'll find the equation for the charge on a capacitor in an RC circuit as a function of time: Q = Q_0 * e^(-t/RC)
To figure out what time you'll have x% of Q_0, just set e^(-t/RC) to .x and solve for t.
The key to the second half is realizing that you'll have 1/sqrt(2) (about 70%) of Q_0 when the U_C is halved--
U_C = Q^2 / 2C
U_C /2 = (Q/sqrt(2))^2 / 2C
(page 952)
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