Inductive Reactance – Reactance of Inductor

An inductor is multiple turns of wire wound to form a coil. It stores energy in the magnetic field as electric current passes through it. It is represented symbolically by the letter ‘L’. Inductors have the inherent ability to oppose changes in current and therefore offer resistance to them. This property of resisting current changes is called inductive reactance. Inductive reactance is denoted by ‘X_L’. The units of X_L are ohms (Ω).

Inductive Reactance

The ability of the opposition to changes in the flow of current in an AC circuit is called inductive reactance. According to Lenz’s law, induced voltage attempts to counteract changes in current. If the current starts decreasing from the present value, the induced voltage polarity will tend to push up the current to resist the decreasing trend. Similarly, if the current starts increasing, the induced voltage polarity tends to push down the current.

The relationship between induced emf and the rate of changing current is expressed as:

Characteristics of Inductor in AC Circuit

Consider the inductor connected in an AC circuit below:

When the supply voltage changes, the inductor induces a self emf known as self-inductance of the coil. The changes in supply voltage lead to changing current and result in an induced emf. The resulting emf swings from maximum to minimum levels rather than remaining constant. This can be illustrated graphically through a phasor diagram.

Phasor Diagram

A phasor diagram represents a phase of voltage, current and self-induced emf with variations in amplitude and frequency.

The phasor diagram shows the displacement of phases between voltage and current. Nearly 90 degrees separate the voltage waveform from the current waveform. Therefore, we may say that in an inductive circuit, voltage always runs 90 degrees behind the current.

Derivation of Inductive Reactance

Considering the same phase shift approach, if the voltage waveform is considered to be at zero degrees, the current will lag at -90 degrees. The voltage waveform will match a sine wave while the current waveform will match a negative cosine waveform.

We can relate current with -90 degrees phase lag as:

The expression of voltage as a sine function at 0 degrees is expressed as:

The expression of induced emf is given by:

Considering V_L=e:

Integrating both sides of the above expression:

Evaluating phase expression at wt = π sin(wt-π/2) equals ‘1’:

Substituting inductive reactance X_L:

The angular frequency is expressed as:

The above expression for inductive reactance X_L:

Example

Calculate inductive reactance for an inductive coil of 250mH connected across 150V, 50Hz AC supply. Determine the current flowing in the circuit:

For inductive reactance:

For current, applying Ohm’s law:

Conclusion

Inductive reactance is a measure of the ability of any inductor to resist the change of current across it. It behaves just like resistance, but it can store energy in the form of a magnetic field when an electric current passes through it.