A-level Physics (Advancing Physics)/Current/delta

The Greek letter delta means 'difference in'. So, in the case of current, it represents the difference in charge divided by the difference in time. If we write it as we would in calculus:

$$I = \frac{dQ}{dt}$$

Without using calculus, we can only take an approximation of I from values as close together as possible on either side of the point at which we wish to calculate the current. By using calculus, we can calculate the exact value of the current at a given point. For example, if Q = 2t (i.e. 1 coulomb every 2 seconds):

$$I = \frac{dQ}{dt} = 1 \times 2t^{1-1} = 2t^0 = 2\mbox{ A}$$