# Inductive Reactance Formulae & Calculations

### In this section

Any inductor will resist the flow of an alternating current due to its inductance.

Even an inductor with zero resistance will resist the flow of current in this way.

The degree to which the inductor impedes the flow of current is due to its inductive reactance.

## Inductive reactance basics

The effect by which the current flow of an alternating or changing current in an inductor is reduced is called its inductive reactance. Any changing current in an inductor will be impeded as a result of the inductance associated with it.

The reason for this inductive reactance can be simply seen by examining the self-inductance and its effect within the circuit.

When a changing current is applied to an inductor, the self-inductance gives rise to an induced voltage. This voltage is proportional to the inductance and as a result of Lenz's law the induced voltage is in the opposite sense to the applied voltage. In this way the induced voltage will work against the voltage causing the current to flow and in this way it will impede the current flow.

## Inductive reactance equations

When a changing signal such as a sine wave is applied to a perfect inductor, i.e. one with no resistance, the reactance impedes the flow of current, and follows Ohms law.

Where:
XL = inductive reactance on ohms, Ω
V = voltage in volts
I = current in amps

The inductive reactance of an inductor is dependent upon its inductance as well as the frequency that is applied.

Where:
XL = inductive reactance on ohms, Ω
π = Greek letter Pi, 3.142
f = frequency in Hz
L = inductance in henries

## R-L circuits and inductive reactance

In reality an inductor will have some resistance, and also inductors may be combined with resistors to make a combined network. As a result of the fact that the current and voltage within an inductor are 90° out of phase with each other (current lags the voltage), inductive reactance and resistance cannot be directly added.

As a result of the fact that the current and voltage in the inductor are out of phase, this means that the resistance and inductive reactance cannot be directly added together.

It can be seen from the diagram that the two quantities need to be added together vectorially. This means that the inductive reactance and resistance each need to be squared, added and then the resultant square root taken:

The resultant combination of resistance and inductive reactance is referred to as impedance and this is again measured in ohms.

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