A Coil That Is a Short Circuit at DC Is 628 Ohms at a Kilohertz

Reactance drops voltage without consuming power

Twelve volts across this coil at 60 hertz drives 0.318 amps, which looks exactly like a 37.7 ohm resistor from the outside — and yet the average power is not the 3.8 watts a resistor would burn. In an ideal inductor the current lags the voltage by a quarter cycle, so the instantaneous power is positive for half of each cycle and negative for the other half: the coil takes energy into its magnetic field and gives all of it back. The 3.8 figure is reactive power, which circulates rather than being consumed, and it is why the electricity meter on a house is happier with a heater than with a large motor drawing the same current.

The same coil is three different components

At mains frequency 100 millihenrys is a mild obstacle you might not notice; at a kilohertz it is a serious one; at a megahertz the same formula gives 628 kilohms, and the coil is effectively an open circuit. Real inductors give up before that, because the winding's own stray capacitance eventually resonates with the inductance and the component starts behaving like a capacitor instead — every inductor has a frequency above which it stops being an inductor. Choosing one therefore means checking that its self-resonant frequency sits well above the band you care about, a specification that datasheets print and beginners routinely skip.

Frequently asked questions

Why does a motor draw a huge current at switch-on?

Because at the instant of starting it is not yet turning, and a turning motor generates a voltage of its own that opposes the supply. Stationary, the only thing limiting the current is the winding's resistance and reactance, which together are far smaller than what the running machine presents. The inrush lasts only as long as the motor takes to come up to speed, but it can be several times the running current, which is why motor circuits use slow-blow fuses and why a large motor starting on a weak supply visibly dips the lights.

How does this combine with resistance in a real circuit?

Not by adding. Resistance and reactance are at right angles to each other in the sense that matters, so the total opposition — the impedance — is the square root of the sum of their squares. A 30 ohm resistor in series with 40 ohms of reactance gives 50 ohms of impedance rather than 70, and the familiar 3-4-5 triangle turns up because the arithmetic is the same. Adding them directly is one of the most common early mistakes in alternating-current work, and it always overstates the opposition, sometimes badly.