Correct Answer

Concept & PrincipleElectricalBasic Electrical

Option A

$2\pi fL$

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

💡 Explanation

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

🔢 Key Formulas

$X_L = 2\pi fL$ — Formula for inductive reactance in Ohms ( $\Omega$ )

$V_L = I_L \cdot X_L$ — Ohm's law applied to an inductor

⚙️ Working Principle

When an AC current flows through an inductor, it creates a time-varying magnetic field, which induces a back electromotive force (EMF) according to Faraday's Law of Induction. This back EMF opposes the change in current, resulting in an effective resistive-like property called reactance. As frequency increases, the rate of change of current increases, strengthening the back EMF and thereby increasing the reactance.

📌 Key Points

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Inductive reactance is measured in Ohms ( $\Omega$ ).
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It is zero for Direct Current (DC) as frequency $f = 0$ .
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It increases linearly with both frequency ( $f$ ) and inductance ( $L$ ).
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The current lags the voltage by $90°$ in a pure inductive circuit.

✅ Advantages

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Essential for filtering and frequency-selective circuits
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Allows for design of ballasts and chokes in power systems

❌ Disadvantages / Limitations

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Causes phase lag in power systems leading to poor power factor
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Inductors are bulky and harder to integrate in compact microelectronics compared to resistors

🛠️ Applications / Uses

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LC Oscillators
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Low-pass and High-pass filters
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Chokes in fluorescent lamps
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Power transmission voltage regulation

📄 Additional Information

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For DC circuits, an ideal inductor acts as a short circuit since $f=0$ implies $X_L=0$ .
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Option B represents the formula for capacitive susceptance or inverse reactance, while Option D ( $\frac{1}{2\pi fC}$ ) is the correct formula for Capacitive Reactance ( $X_C$ ).

📊 Diagram / Illustration

✅

A is correct — The inductive reactance $X_L$ is mathematically defined as $2\pi fL$ , representing the opposition to current flow in an AC circuit due to magnetic field changes.

Core Concepts Used

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Faraday's Law of Induction Lenz's Law AC Circuit Theory

💡 EXAM TIP

Always remember that inductive reactance ( $X_L$ ) increases with frequency, whereas capacitive reactance ( $X_C$ ) decreases as frequency increases; this is a favorite topic for GATE/IES exams.

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