Question

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?

Answer 1

Answer:

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.