An inductor L and resistor R are connected in series across a steady DC voltage V. What is the steady-state current?

When an inductor ($L$) and resistor ($R$) are connected in series across a constant DC voltage source ($V$), the current follows the transient response $i(t) = \frac{V}{R} \left(1 - e^{-t/\tau}\right)$. Under steady-state DC conditions ($t \to \infty$), the rate of change of current becomes zero ($\frac{di}{dt} = 0$), so the inductor behaves as an ideal short circuit ($V_L = 0$). The steady-state current is therefore limited solely by the resistor: $I = \frac{V}{R}$.

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