Circuits & Electrical Power · Inductors
The coil divides where the capacitor multiplied
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The coil divides where the capacitor multiplied

An inductor is a coil that resists a CHANGE in current. Switch it on and the current climbs rather than jumping; switch it off and the collapsing field will do something spectacular to your contacts if nothing is there to catch it.

τ=LR\tau = \dfrac{L}{R} — read aloud tau equals L over R. τ\tau is the time constant in seconds, LL is the inductance in henries, and RR is the total circuit resistance in ohms. Note the shape and note it hard: the capacitor MULTIPLIED its two components, the inductor DIVIDES. It is the same τ\tau, the same seconds, the same 37%-after-one and gone-after-five — but the arithmetic is upside down, and mixing the two is this lesson's named trap. The reason is physical: resistance drags a capacitor's discharge out, but it hurries an inductor's current to its final value.

And the coil banks energy too, in its magnetic field rather than an electric one: E=12LI2E = \tfrac{1}{2} L I^{2}, E equals half L I squared, with EE in joules, LL in henries and II the steady current through the coil, in amperes. The shape is the capacitor's energy relation with volts swapped for amps, ½ and square intact — which is the tidiest analogy in first-year circuits and worth carrying.

The units will catch the swapped time constant if you let them. Henries over ohms is seconds; henries TIMES ohms is not. Push the units through the rearrangement every time — if they refuse to cancel into the answer's units, the rearrangement is wrong, no appeal. Units that do work out never prove you right, though. The check runs one way.