Acurrent exists whenever electric charges move. if δq is the net charge that passes through a surface during a time period δt, then the average current during this time interval is defined as average current = δq δt = q2 − q1 t2 − t1 . if we take the limit of this average current over smaller and smaller time intervals, we get what is called the current i at a given time t1: i = lim δt→0 δq δt = dq dt . thus the current is the rate at which charge flows through a surface. the current in a wire is defined as the derivative of the charge: i(t) = q'(t). what does b i(t) a dt represent? it represents the change in the charge q from time t = a to t = b. it represents the current i at time t. it represents the change in the current i from time t = a to t = b. it represents the charge q at time t.