Final answer:
The question involves finding the time-dependent current i(t) in an electrical circuit and involves understanding the exponential growth characteristic of electric circuits with inductances or capacitances.
Step-by-step explanation:
The student's question asks to find i(t) for t > 0 in an electrical circuit, which involves exponential behavior typically described in the context of electric circuits containing inductances or capacitances. The formula to find the current at any given time t after the switch has been operated is given by I = I0(1 - e-t/τ), where I0 is the final steady-state current and τ is the inductive time constant of the circuit.
As described in the reference material, in the first period of t, the current i(t) rises to 0.632 of the final value I0. Continuing with the process in steps, at various multiples of the characteristic time τ, it can be seen that the current reaches further fractions of the steady state. This is known as an exponential growth and can be depicted in a plot, as mentioned in the references.