Question

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 $dQ/dt$ the rate of charge flow. What is the current to a $10\mu \mathrm{F}$ capacitor whose voltage is increasing at the rate of $2.0\mathrm{V}/\mathrm{s}$?

Short answer

The current to a $10\mu F$capacitor whose voltage is increasing at the rate of$2.0V/S$is$20\mu A.$

Step-by-step solution

Given Information

Rate of charge flow $=dQ/dt$

Capacitor$=10\mu F$

Voltagerole="math" localid="1648643337782" $=2.0V/S$

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,

$C=\frac{q}{U}$

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

$C=\frac{q/t}{U/t}$

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

$C=\frac{dq/dt}{dU/dt}$

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

$I:=\frac{dq}{dt}.$

This means that we can write the current as

$I=C\frac{dU}{dt}$

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

Then the numerical solution will be

localid="1648643685911" $I=(10\mu F·{10}^{-6}\times 2.0V/S)$

Multiply the expression,

$=20\mu \mathrm{A}$

Final Answer 

Hence, the current to a $10\mu F$capacitor whose voltage is increasing at the rate of $2.0\mathrm{V}/\mathrm{S}$is $20\mu \mathrm{A}$.