3.2 ELECTRIC CURRENT

Imagine a small area held normal to the direction of flow of charges. Both the positive and the negative charges may flow forward and backward across the area. In a given time interval $t$, let $q_{+}$ be the net amount (i.e., forward minus backward) of positive charge that flows in the forward direction across the area. Similarly, let $q_{-}$ be the net amount of negative charge flowing across the area in the forward direction. The net amount of charge flowing across the area in the forward direction in the time interval t, then, is $q=q_{+}-q_{-}$. This is proportional to $t$ for steady current and the quotient

$$I=\frac{q}{t}$$(3.1)

is defined to be the current across the area in the forward direction. (If it turn out to be a negative number, it implies a current in the backward direction.)

Currents are not always steady and hence more generally, we define the current as follows. Let $\mathrm{\Delta }Q$ be the net charge flowing across a crosssection of a conductor during the time interval $\mathrm{\Delta }t$ [i.e., between times $t$ and ($t+\mathrm{\Delta }t$)]. Then, the current at time $t$ across the cross-section of the conductor is defined as the value of the ratio of $\mathrm{\Delta }Q$ to $\mathrm{\Delta }t$ in the limit of $\mathrm{\Delta }t$ tending to zero,

$$I(t)\equiv \underset{\mathrm{\Delta }t\to 0}{lim}\frac{\mathrm{\Delta }Q}{\mathrm{\Delta }t}$$(3.2)

In SI units, the unit of current is ampere. An ampere is defined through magnetic effects of currents that we will study in the following chapter. An ampere is typically the order of magnitude of currents in domestic appliances. An average lightning carries currents of the order of tens of thousands of amperes and at the other extreme, currents in our nerves are in microamperes.