Introduction:

When an alternating current (AC) voltage is applied to an inductor, the behavior of the circuit differs from that of a resistor. Inductors oppose changes in current due to self-induced emf, leading to a phase difference between voltage and current. This concept is essential in AC circuit analysis and finds applications in transformers, motors, and various electronic circuits.

AC Voltage Across an Inductor:

An inductor is a coil of wire that resists changes in current due to electromagnetic induction. When an AC voltage is applied across an inductor, the current flowing through it does not immediately follow the voltage but lags behind by 90°.

Mathematical Representation:

Using Kirchhoff’s Voltage Law (KVL), the equation for an AC circuit with an inductor is:

V = L (dI/dt)

For an AC source:

V = V₀ sin(ωt)

Solving for current:

I = (V₀ / ωL) sin(ωt - 90°)

This shows that current lags voltage by 90 degrees (π/2 radians).

Read Also: Class 12 Physics Transformers - Study Notes, Working, Uses

Inductive Reactance (XL):

Inductive reactance (X_L) is the opposition offered by an inductor to AC, given by:

X_L = ωL = 2πfL

where:

- f = frequency of AC (Hz)

- L = inductance (H)

The higher the frequency, the greater the opposition to current.

Phase Difference Between Voltage and Current:

- Voltage leads the current by 90° in a purely inductive circuit.

- This phase shift is crucial in AC circuit analysis and power calculations.

Power in an Inductive Circuit:

The instantaneous power is given by:

P = VI = V₀ sin(ωt) × I₀ sin(ωt - 90°)

Since sin(ωt - 90°) = -cos(ωt),

P = V₀ I₀ sin(ωt) (-cos(ωt))

Average power over a full cycle is zero, meaning no real power dissipation in a pure inductor. Energy is stored and released in the magnetic field.

Applications of Inductors in AC Circuits:

1. Transformers – Work on the principle of electromagnetic induction.

2. Motors and Generators – Use inductors to create magnetic fields.

3. Radio Tuning Circuits – Inductors filter and select desired frequencies.

4. Power Supplies – Inductive filters smooth out fluctuations.

Conclusion:

When AC voltage is applied to an inductor, the current lags behind the voltage by 90°, and the inductor opposes changes in current through inductive reactance. Inductors play a key role in AC circuits, from power distribution to communication systems. Understanding their behavior is essential for mastering electromagnetism and AC circuit analysis in Class 12 Physics.