A current 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 charge Q from time t = a to t = b
Explanation:
As given in the question the current is defined as the derivative of charge.
I(t) = dQ(t)/dt ..... (i)
But if we take the inegral of the equation (i) for the time interval from t=a to
t =b we get
Q =∫_a^b▒〖I(t) 〗 dt
which shows the change in charge Q from time t = a to t = b. Form here we can say that, change in charge is defiend as the integral of current for specific interval of time.
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