Impedance of a Coil
If a direct current is passed through a coil, the resistance of the coil to the passing of current through it is the nsame as if the coil were stretched into a straight wire. If an alternating vurrent is passed through the coil, the resistance of the coil is quite different.
If an alternating voltage is applied across the ends of the coil, an alternating current is induced. The alternating current induces an EMF across the ends of the coil, but the direction of the induced EMF opposes the change causing it – the changing current, so that if the current is increasing, to the right, the induced EMF is increasing to the left. We can write the relationship between the induced EMF.
is a constant called the inductance of the coil. The inductance of the coilis a property of the coil construction – the number of turns, the material on which the coil is wound and the space inside the coil.
Because the induced EMF opposes the current passing through it, it also opposes the voltage applied across it. If the applied voltage, and so the current, is sinusoidal, we can writeso thatandThe induced EMF increases with the frequency of the applied voltage, and so will the apparent resistance of the coil to the passing of current through it.
The resistance of the coil to alternating current is labelledand is called the reactance of the coil. The reactance is related to the inductance via the equation
Withdefined this way we can rewrite Ohm's Lawfor the current passing through a coil asor
This equation holds for the RMS values ofandsoand the peak values of andso that