For a series RL circuit with a step input Vs, which expression gives the current i(t) for t ≥ 0?

• A. i(t) = (Vs/R) e^{-tR/L}
• B. i(t) = (Vs/R) t
• C. i(t) = (Vs/R) (1 - e^{-tR/L})
• D. i(t) = Vs/R

Answer: (C)

When a series RL circuit sees a sudden voltage step, the inductor resists a rapid change in current, so the current starts at zero (assuming the inductor is unenergized) and then rises toward a steady value of Vs/R. The circuit is governed by L di/dt + R i = Vs, a first‑order differential equation. Solving it with i(0) = 0 gives i(t) = (Vs/R) [1 − e^{−(R/L) t}], which shows the current approaching the final value Vs/R with a time constant τ = L/R. This form correctly captures both the initial condition and the exponential approach to the steady state. The other forms fail because they either start from the wrong initial value, grow without bound, or omit the transient behavior entirely.