College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Question

When a capacitor is placed in an alternating-current (AC) circuit, the charge on its plates varies with time according to the function shown below.

q(t) = 59cos(1880 · t) µC

(Here t is in seconds.) What is the current i(t) flowing through this capacitor as a function of time?
[N.B.: Note the power-of-ten prefixes on the units!]

Expert Solution
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Step 1

The current flowing through a capacitor is related to the rate of change of charge on its plates, which can be expressed as:

i(t) = C * (dq/dt)

where C is the capacitance of the capacitor and dq/dt is the derivative of the charge function with respect to time.

In this case, the charge function is:

q(t) = 59cos(1880 · t) µC

Taking the derivative with respect to time, we get:

dq/dt = -104,920sin(1880 · t) nC/s

 

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