RL circuit
Put a resistor and an inductor together in a circuit and the current can no longer jump instantly — it eases in and eases out along a smooth curve. An RL circuit is where you watch this gradual build-up and decay. It answers the question: how fast does the current in a coil actually turn on and off?
Precisely, when a battery of voltage V is switched onto a resistor R and inductor L in series, the current grows as I(t) = (V/R)(1 - e^(-t/tau)), climbing toward its final value V/R. The time constant tau = L/R, in seconds, sets the pace: after one tau the current has reached about 63% of full, and after roughly 5 tau it is essentially there. When the source is removed, the current decays away as I(t) = I_0 e^(-t/tau).
RL circuits appear wherever coils switch: relays, motors, power supplies, and spark suppressors. The honest point is that this is the magnetic twin of the RC circuit, where a capacitor charges through a resistor — both give the same exponential shape, but here it is the inductor, not a capacitor, that opposes sudden change. Opening the switch too fast makes dI/dt huge, so L dI/dt can spike to a big voltage and arc across the contacts.
With L = 2 H and R = 10 ohm, the time constant is tau = L/R = 0.2 s. The current reaches about 63% of its final value in 0.2 s and is nearly steady after about 1 s.
L = 2 H and R = 10 ohm give a 0.2 s time constant.
Suddenly breaking an RL circuit forces dI/dt to be huge, so L dI/dt can spike to hundreds of volts — the spark seen across an opening switch. This is why inductive loads need protection diodes.