Inductors connect current change to voltage

Current carries the stored state

For an ideal inductor, voltage is $v=L\,di/dt$ and energy is $E=Li^2/2$. Its current cannot jump instantly without an impulse of voltage. At settled DC, an ideal inductor has zero voltage and behaves as a short circuit. A real winding retains resistance and has current-dependent core behavior, so “short at DC” does not mean a lossless wire at any current.

Applying a constant 1 V across 10 mH changes current at 100 A/s. Starting from zero, current rises by 100 mA in 1 ms if the voltage remains constant. Stored energy at 100 mA is $0.01\times0.1^2/2=50$ μJ. A continuing ramp eventually meets source or component limits; the ideal formula alone does not create a safe maximum current.

Add a resistor

Connect a 3.3 V step to a series 330 Ω resistor and 10 mH inductor. The final current is 10 mA, and the time constant is $\tau=L/R=30.303$ μs. Starting from zero, $i(t)=10\text{ mA}(1-e^{-t/\tau})$. After one time constant, current is 6.3212 mA. The inductor initially takes the full source voltage; its voltage tends toward zero as current settles.

Compare this with the capacitor: capacitor voltage and inductor current are the quantities that remain continuous in finite-source switching. Keeping track of the correct stored state prevents a common error in initial-condition problems.

Opening a path changes the model

If an inductor carrying current is abruptly disconnected, it develops voltage to continue current through whatever parasitic or protective path exists. A flyback diode is a common deliberate path, but its voltage, energy, and decay behavior require a circuit calculation. Do not conclude that an open switch immediately makes stored current zero.

When simulating an RL transition, include series resistance and a physically meaningful current-return path. State whether winding resistance is included in R. A 30.303 μs prediction from nominal values is useful only if the actual total series resistance and inductance match those assumptions.