Final answer:
To determine the inductor current for t > 0 in a circuit, perform a transient response analysis in the time domain utilizing the natural response and equations specific to inductors. The time constant is critical in such calculations and precise exponential treatment helps achieve accurate results concerning how quickly current reaches a certain percentage of its final value.
Step-by-step explanation:
To find the inductor current for t > 0 in a given circuit, it is necessary to conduct a transient response analysis in the time domain. This involves using the natural response of the circuit and applying Kirchhoff's laws along with the defining equations for inductors, which relate the voltage across the inductor to the rate of change of current through it using VL(t) = -L(dI/dt). The time constant (τ) of an RL circuit is given by τ = L/R, where L is the inductance and R is the resistance in the circuit. To analyze the current at specific instances such as t = 0, t = 2.07, and as t → ∞, one can use formulas that include the exponential factor e expressed as I(t) = I0e-t/τ, where I0 is the initial current.
Additionally, to find the time for a current through an inductor to reach or decline to a certain percentage of its final or initial value, we also use the exact exponential treatment and compare the results with an approximate method using integral multiples of the time constant. Significant differences may suggest that precise calculations are necessary for accurate predictions in certain engineering applications.