Q. 69

Expert-verified
Found in: Page 741

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

A capacitor being charged has a current carrying charge to and away from the plates. In the next chapter we will define current to be the rate of charge flow. What is the current to a capacitor whose voltage is increasing at the rate of ?

The current to a capacitor whose voltage is increasing at the rate of is

See the step by step solution

Step 1: Given Information

Rate of charge flow

Capacitor

Voltage

Step 2: Explanation

We know from the definition that capacitance is the ratio of the potential charge to the difference between the potentials across the capacitor. That is,

If we divide both the denominator and numerator by the time, we can write

or, more specifically, if we take the infinitesimal changes of the charge and potential difference, we can write

Let us not forget that the change of charge per unit time is nothings less but the current ; that is,

This means that we can write the current as

We know the capacitance, and we know the rate of change of the potential difference as well.

Then the numerical solution will be

Multiply the expression,

Step 3: Final Answer

Hence, the current to a capacitor whose voltage is increasing at the rate of is .