0
$\begingroup$

Current is defined as the amount of charge passing a given point per unit time. The word amount throws me off. sorry if this question seems dumb, but

why can current not be equal to integral of charge from time t=t1 to t2?

enter image description here

since we want to know the amount of charge passing a given point, we can add up charge from time t1 until time t2

$\endgroup$
  • 1
    $\begingroup$ Compare this to kinematics: "$\Delta x$ is defined as the amount of change in position. So $\Delta x = \int x \, dt$, since we want to know the amount of change in position, we add up the position." $\endgroup$ – knzhou Oct 8 '18 at 15:59
  • $\begingroup$ You defined current as for 'per unit time' . Hope you have got enough hint.. $\endgroup$ – Jnan Oct 8 '18 at 16:00
0
$\begingroup$

Current is defined as the amount of charge passing a given point per unit time.

In fact, electric current is defined as the flow of electric charge. From the Wikipedia article Electric current

An electric current is a flow of electric charge.

From the Britannica article Electric current

Electric current is a measure of the flow of charge

A flow is a rate, i.e., an amount over an elapsed time. If an amount of electric charge $\Delta Q$ flows into a region in some time $\Delta t$, then there is an electric current into the region (with an average value of)

$$\bar{I} = \frac{\Delta Q}{\Delta t}$$

In the electric circuit context, we have a circuit law (Kirchhoff's Current Law) that requires the current into a region equal the current out of the region and so we can think of the current through the region, e.g., the body of a resistor.

$\endgroup$
0
$\begingroup$

This is because current is strictly defined as the rate at which charge passes through a given cross sectional area of a conductor. Here, we are required to measure "how many" charges cross the perpendicular cross section in a given time, therefore derivative is used here as a 'rate measurer'.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.