Question

Using the exact exponential treatment, find how much time is required to discharge a $250\textrm{ }\mu\textrm{F}$ capacitor through a
$500\textrm{ }\Omega$ resistor down to 1.00% of its original voltage.

Final Answer

$0.576\textrm{ s}$

### Solution video

# OpenStax College Physics for AP® Courses, Chapter 21, Problem 72 (Problems & Exercises)

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Video Transcript

This is College Physics Answers with Shaun Dychko. Given an

*RC*circuit with a resistance of 500 ohms and a capacitance of 250 microfarads, which is 250 times 10 to the minus 6 farads and a final voltage divided by initial voltage of one percent, which is 0.0100, how much time is needed for the voltage to reach this one percent? So the voltage on a disc charging capacitor is the initial voltage times*e*to the negative time divided by resistance times capacitance and we will divide both sides by*V naught*to get*e*to the negative*t*over*RC*equals*V*over*V naught*and then take the natural logarithm of both sides and the natural logarithm of*e*to the something is just that something so we have negative*t*over*RC*equals the right hand side natural logarithm of*V*over*V naught*. Then we'll multiply both sides by negative*RC*to solve for*t*and we get the time then is negative resistance times capacitance times natural logarithm of this ratio. So that's negative 500 ohms times 250 times 10 to the minus 6 farads times 0.0100 and that is 0.576 seconds.