Correct Answer

Concept & PrincipleElectricalBasic Electrical

Option B

$V = i X_L$

Quick Summary: In an AC circuit containing only a pure inductor, the voltage drop across the inductor is governed by its inductive reactance. The relationship is expressed as $V = i X_L$, where $V$ is the RMS voltage, $i$ is the RMS current, and $X_L$ is the inductive reactance.

💡 Explanation

In an AC circuit containing only a pure inductor, the voltage drop across the inductor is governed by its inductive reactance. The relationship is expressed as $V = i X_L$ , where $V$ is the RMS voltage, $i$ is the RMS current, and $X_L$ is the inductive reactance.

🔢 Key Formulas

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

$V = i X_L$ — Ohm's Law analogue for inductive AC circuits

⚙️ Working Principle

An inductor resists changes in current through self-induction, creating a counter-electromotive force (back EMF). The inductive reactance $X_L$ is defined as $X_L = 2\pi f L$ , representing the opposition to current flow in an AC circuit. In a pure inductive circuit, current lags behind the voltage by an angle of $90°$ (or $\frac{\pi}{2}$ radians).

📌 Key Points

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In a pure inductor, the voltage leads the current by exactly $90°$ .
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Inductive reactance ( $X_L$ ) is directly proportional to frequency ( $f$ ) and inductance ( $L$ ).
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Pure inductors do not consume real power; they only exchange reactive power.
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The SI unit for inductive reactance is Ohms ( $\Omega$ ).

✅ Advantages

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Used in tuning circuits for radio and telecommunications.
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Essential for filtering signals and noise suppression.

❌ Disadvantages / Limitations

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Causes lagging power factor in electrical grids.
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Pure inductors are theoretical; real inductors have parasitic resistance.

🛠️ Applications / Uses

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Power factor correction units.
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Frequency-selective filters in electronic circuits.

📄 Additional Information

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Option A ( $V=iR$ ) describes a resistor, where voltage and current are in phase.
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Option C ( $V=iX_C$ ) describes a capacitive circuit, where current leads voltage by $90°$ .
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Option D ( $V=iL_C$ ) is physically incorrect as $L_C$ is not a standard electrical parameter.

📊 Diagram / Illustration

✅

B is correct — The voltage in a pure inductive circuit is the product of current and inductive reactance ( $V = i X_L$ ).

Core Concepts Used

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Self-Induction Inductive Reactance AC Circuit Analysis

💡 EXAM TIP

Always remember the mnemonic 'ELI' (Voltage E leads Current I in L) to quickly identify phase relationships in AC circuits.

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