Electric Current

To define current precisely, imagine an idealised 'gas' containing both positively and negatively charged particles, moving randomly in every direction, all of them able to cross some fixed imaginary flat plane P (Fig. 11.1). In a time interval $t$, let $q_+$ be the total positive charge that crosses P moving in a chosen forward direction, and let $q_-$ be the total negative charge that crosses P also moving in that same forward direction. The net charge that has flowed in the forward direction is then $q=q_+-q_-$ (charge moving backward effectively subtracts from the forward count).

For a STEADY flow, this net charge $q$ is directly proportional to the time $t$ over which it is measured, and the ratio $q/t$ is defined as the electric current $I$:

The SI unit of current is the ampere (A); charge is measured in coulomb (C) and time in second (s), so $1\,\text{A}=1\,\text{C/s}$.

If the current is not steady but varies with time, this average definition is no longer adequate. Instead, let $\Delta q$ be the small amount of net charge that crosses the plane P during a short time interval $\Delta t$ (from time $t$ to $t+\Delta t$). The INSTANTANEOUS current at time $t$ is then defined as the limiting value of this ratio as $\Delta t$ shrinks to zero:

$I(t)=\lim_{\Delta t\to 0}\frac{\Delta q}{\Delta t}\qquad\text{--- (11.2)}$ …