Question

A 20.0 Hz, 16.0 V source produces a 2.00 mA current when connected to a capacitor. What is the capacitance?

Final Answer

$0.995\textrm{ }\mu\textrm{F}$

### Solution video

# OpenStax College Physics for AP® Courses, Chapter 23, Problem 86 (Problems & Exercises)

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Video Transcript

This is College Physics Answers with Shaun Dychko. A 16.0 volt source with a frequency of 20.0 hertz is connected to a capacitor and the current in this circuit is 2.00 milliamps, which is 2.00 times 10 to the minus 3 amps and the question is what must be the capacitance then of the capacitor? So the current is going to be the voltage divided by the capacitive reactance and the capacitive reactance is 1 over 2

*π*times frequency times capacitance. We are going to divide*V*by this fraction which is the same as multiplying by its reciprocal so I am gonna flip the fraction and multiply by that flipped version— the reciprocal in other words— and so we have current then is*V*times 2*πfC*and we can solve this for*C*by dividing both sides by*V2πf*. So the capacitance then is the current divided by the voltage times 2*π*times the frequency. That's 2.00 times 10 to the minus 3 amps divided by 16.0 volts times 2*π*times 20.0 hertz which is 0.995 microfarads is the capacitance.