# “why is current the derivative of charge and not integral of charge?”

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

• 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." – knzhou Oct 8 '18 at 15:59
• You defined current as for 'per unit time' . Hope you have got enough hint.. – Jnan Oct 8 '18 at 16:00

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.

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'.