Inductive reactance is calculated by

Question

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$2\pi fL$

Explanation: Inductive reactance ($X_L$) is the opposition offered by an inductor to the flow of alternating current. It is directly proportional to both the frequency of the supply and the inductance of the coil.

Working Principle: When an AC voltage is applied across an inductor, it produces a changing magnetic field that induces a back electromotive force (EMF) according to Lenz's Law. This back EMF opposes the change in current. The opposition, quantified as $X_L = 2\pi fL$, increases as the rate of change of current (frequency) or the magnetic storage capability (inductance) increases.

Key Formulas: $X_L = 2\pi fL$ — Formula for Inductive Reactance in ohms ($\Omega$); $V_L = I \cdot X_L$ — Ohm's law equivalent for inductive circuits

Key Points: Inductive reactance is measured in Ohms ($\Omega$).; It is directly proportional to frequency ($X_L \propto f$).; For DC circuits ($f=0$), $X_L = 0$, meaning an ideal inductor acts as a short circuit.; The current in a pure inductor lags the voltage by $90^\circ$.

Advantages: Useful for filtering high-frequency noise in circuits.; Essential for energy storage in magnetic fields.

Disadvantages: Causes phase lag between voltage and current.; Not suitable for blocking DC current in power electronics without considering resistance.

Applications: Tuned circuits and oscillators.; Power supply smoothing filters.; Ballasts in fluorescent lighting.

Additional Info: In a DC circuit, frequency $f = 0$, so $X_L = 0$.. Option B represents the reciprocal, which is the formula for Capacitive Reactance ($X_C$).. Option C is dimensionally incorrect for reactance.. Option D is the correct formula for Capacitive Reactance ($X_C$).

Answer: A is correct — The inductive reactance of a coil is mathematically defined as the product of $2\pi$, supply frequency, and inductance.

Exam Tip: Always remember: Inductive Reactance ($X_L$) increases with frequency, whereas Capacitive Reactance ($X_C$) decreases as frequency increases. This inverse relationship is frequently tested in filter design questions.

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