Think of it this way adder: Suppose you have a very large coil wound on a very large iron core. Our hypothetical inductor is many Henries in value. This inductor is wired in series with an incandescent light bulb, a SPDT switch and a DC power supply. When the switch is thrown in one direction, the power supply is switched in and the circuit is complete. When the switch is thrown the other way, the power supply is switched OUT of circuit and the switch itself completes the circuit. Now we simply have the large inductor and the incandescent light bulb hooked together.
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Start out with the power supply switched out of circuit. Nothing unusual here. Now, throw the switch to switch in the power supply. The light will not come on instantly. Inductors oppose a change in current. It takes a specific amount of time for the magnetic field to build to the point where it is the full load current drawn by the light bulb. At the instant the switch was thrown, the FULL supply voltage was across the inductor and NO current flowed. As the field grew, the current gradually climbed and the voltage across the inductor gradually diminished to zero. Now think about this, while the current was increasing and the voltage across the inductor was decreasing, some power had to be absorbed in the inductor because the inductor had a voltage across it in the same instant that it had current flowing through it. If you were to plot the voltages and currents in this circuit you would find that more power was delivered by the power supply than ever reached the light bulb. Some power was lost in this transition from power supply switched out to power supply switched in. But it wasn't actually lost.
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Here's why: When you switch the power supply out and replace it with a short circuit, the magnetic field in the inductor will fall and continue to supply the light bulb with power. Remember, inductors oppose a change in current. So it will try to continue the current flowing in the circuit. By the time the field has fallen all the way to nothing, you will have gotten back all of the power that was apparently absorbed in the inductor. This is why it's called apparent power. This explanation is very simplified and ignores losses. But I feel it explains it very well.