Correct Answer

Concept & PrincipleElectricalBasic Electrical

Option A

$X_L$

Quick Summary: In an A.C. circuit, inductive reactance ($X_L$) is directly proportional to frequency ($f$). As frequency increases, the rate of change of current through an inductor increases, leading to a greater counter-electromotive force, which manifests as higher opposition to current flow.

💡 Explanation

In an A.C. circuit, inductive reactance ( $X_L$ ) is directly proportional to frequency ( $f$ ). As frequency increases, the rate of change of current through an inductor increases, leading to a greater counter-electromotive force, which manifests as higher opposition to current flow.

🔢 Key Formulas

$X_L = 2\pi f L$ — Inductive Reactance formula

$X_C = \frac{1}{2\pi f C}$ — Capacitive Reactance formula

⚙️ Working Principle

The inductive reactance is defined by the formula $X_L = 2\pi f L$ . Because $f$ is in the numerator, any increase in the supply frequency results in a linear increase in inductive reactance, assuming the inductance ( $L$ ) remains constant. Conversely, capacitive reactance $X_C = \frac{1}{2\pi f C}$ decreases as frequency increases.

📌 Key Points

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Inductive reactance ( $X_L$ ) increases linearly with frequency.
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Capacitive reactance ( $X_C$ ) decreases inversely with frequency.
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Resistance ( $R$ ) is generally considered independent of frequency in an ideal resistor.

✅ Advantages

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Used in tuning circuits for frequency selection.
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Essential for designing high-pass and low-pass filters.

❌ Disadvantages / Limitations

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High frequencies lead to significant skin effect losses in inductors.
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Parasitic capacitance can distort high-frequency performance.

🛠️ Applications / Uses

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Radio frequency (RF) tuning circuits.
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Induction heating systems.
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Power system harmonic filtering.

🔄 Comparison Table

Feature	Inductive Reactance	Capacitive Reactance
Frequency Dependency	Directly Proportional	Inversely Proportional

📄 Additional Information

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Skin effect causes the effective resistance of conductors to increase at very high frequencies, though purely ohmic resistance ( $R$ ) is defined as constant.
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Option B ( $X_C$ ) is incorrect because it is inversely proportional to frequency.
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Option C ( $R$ ) is incorrect as pure resistance does not change with frequency.

📊 Diagram / Illustration

✅

A is correct — Inductive reactance ( $X_L$ ) increases directly with an increase in frequency as governed by the formula $X_L = 2\pi f L$ .

Core Concepts Used

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Inductive Reactance Frequency dependence in A.C. circuits A.C. Series Circuit behavior

💡 EXAM TIP

Remember the mnemonic 'ELI the ICE man': for an Inductor (L), E leads I; for a Capacitor (C), I leads E. Their reactances follow inverse frequency trends ( $X_L \propto f$ and $X_C \propto 1/f$ ).

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