AC Inductance and Inductive Reactance – Working Principle and AC Behavior of Inductors

Introduction

When an inductor is connected to an AC supply, the current flowing through its winding produces a self-induced electromotive force (EMF). This back EMF always opposes the applied voltage that created the current in the first place (Lenz’s Law).

In an AC circuit, an inductor acts as an opposition to time-varying current. This opposition is not only due to resistance, but also due to the inductance of the coil. To achieve maximum inductance, coils are generally wound around an air core or a ferromagnetic (iron) core.

When voltage is applied across the terminals of an inductor, a magnetic field is created and energy is stored in this field. The magnitude of the back EMF depends on how fast the current is changing. This relationship is expressed as:

V_L ∝ (di / dt)

Once the self-induced EMF falls to zero, the current reaches its maximum steady-state value (after approximately five time constants). At this point, in a DC circuit, the inductor behaves like a short circuit because no back EMF is present.

Behavior of an Inductor in an AC Circuit

The behavior of an inductor in an AC circuit is very different from that in a DC circuit. In AC, the applied voltage continuously changes polarity. Therefore, the resistance to current flow depends on both the inductance of the coil and the frequency of the supply.

This opposition to AC is called reactance. Because the component is an inductor, the reactance is known as inductive reactance and is represented by the symbol X_L. Although it is measured in ohms (Ω), it is different from simple resistance (R).

Inductive Reactance

Inductive reactance is given by the formula:

X_L = 2πfL

Where:

• X_L = Inductive Reactance in ohms (Ω)
• π = 3.142 (constant)
• f = Frequency in hertz (Hz)
• L = Inductance in henries (H)

Since angular frequency is given by ω = 2πf, the above equation can also be written as:

X_L = ωL

This equation shows that inductive reactance is directly proportional to both frequency and inductance. As frequency increases, the inductive reactance also increases.

Phase Relationship of Voltage and Current

In a pure inductive circuit (with no resistance), the back EMF opposes the rise and fall of current whenever a sinusoidal voltage is applied. Due to this opposition, the current cannot change instantly.

As a result, the current lags the voltage by 90° (one-quarter cycle). This means that the applied voltage reaches its maximum value one-fourth of a cycle before the current reaches its maximum value.

In other words, in a purely inductive circuit:

Voltage leads current by 90°

Conclusion

AC inductance plays an important role in limiting and controlling alternating current. The resulting inductive reactance depends on frequency and inductance, and it causes a phase difference between voltage and current. Due to these properties, inductors are widely used in filters, transformers, tuning circuits, power supplies, and signal processing systems.