# When Pure Inductor is Connected Across AC Supply

When a pure inductor (a coil with inductance and negligible resistance) is connected across an AC (alternating current) supply, several important electrical characteristics come into play. These characteristics depend on the frequency of the AC supply, the inductance of the coil, and the amplitude of the voltage.

## When Pure Inductor is Connected Across AC Supply

1. Impedance of the Inductor: The impedance of an inductor in an AC circuit is given by the formula Z = jωL, where Z is the impedance, j represents the imaginary unit, ω is the angular frequency (equal to 2π times the frequency of the AC supply), and L is the inductance of the coil. This impedance is purely imaginary and increases linearly with frequency.
2. Phase Shift: When an inductor is connected to an AC supply, it introduces a phase shift between the voltage across the inductor and the current flowing through it. This phase shift is typically 90 degrees or π/2 radians. The voltage across the inductor lags behind the current by this phase angle.
3. Reactance: The reactance of the inductor, which is the AC counterpart to resistance in a DC circuit, is given by X_L = ωL. Reactance depends on the frequency of the AC supply and the inductance of the coil. It increases linearly with frequency.
4. Current Lags Voltage: Because of the phase shift, the current through the inductor lags behind the voltage across it. In other words, the current reaches its maximum value slightly after the voltage peaks in a sinusoidal AC waveform.
5. Voltage Drop: In an ideal pure inductor, there is no resistance, so there is no voltage drop due to resistive losses. However, there is a voltage drop across the inductor due to its inductive reactance, which is in phase with the current.
6. Energy Storage: An inductor stores energy in its magnetic field as current flows through it. When the current decreases or increases, energy is transferred between the source and the inductor’s magnetic field. This energy storage property is used in various electrical and electronic applications.
7. Inductive Kickback: When an inductive load is suddenly disconnected from the AC supply (for example, when a switch is opened), it can generate a voltage spike due to the collapse of the magnetic field. This is known as inductive kickback, and it can be problematic in some circuits, necessitating protective measures.

In summary, when a pure inductor is connected across an AC supply, it primarily exhibits impedance, introduces a phase shift between voltage and current, and stores energy in its magnetic field. The behavior of the inductor depends on the frequency of the AC supply and its inductance. These characteristics are fundamental in AC circuit analysis and are utilized in the design of various electrical and electronic systems.