Answered: When a capacitor is placed in an…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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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

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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