Correct Answer

Concept & PrincipleElectricalBasic Electrical

Option C

Quick Summary: In an RL series circuit, the presence of both resistance and inductance causes the current to lag behind the applied voltage by an angle $\phi$. This phase angle $\phi$ is strictly between $0^\circ$ and $90^\circ$, determined by the ratio of inductive reactance to resistance.

💡 Explanation

In an RL series circuit, the presence of both resistance and inductance causes the current to lag behind the applied voltage by an angle $\phi$ . This phase angle $\phi$ is strictly between $0°$ and $90°$ , determined by the ratio of inductive reactance to resistance.

🔢 Key Formulas

$\phi = \arctan(\frac{X_L}{R})$ — Phase angle calculation

$Z = \sqrt{R^2 + X_L^2}$ — Total circuit impedance

⚙️ Working Principle

In a purely resistive circuit, the phase angle is $0°$ , and in a purely inductive circuit, it is $90°$ . An RL series circuit behaves as a combination of both elements. The impedance triangle, formed by $R$ on the horizontal axis and $X_L$ on the vertical axis, dictates the phase angle $\phi = \arctan(\frac{X_L}{R})$ , which remains strictly within the first quadrant.

📌 Key Points

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Current always lags voltage in an RL circuit.
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The power factor $\cos \phi$ is always lagging and less than 1.
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At $R = 0$ , the angle reaches $90°$ (purely inductive).
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At $X_L = 0$ , the angle reaches $0°$ (purely resistive).

✅ Advantages

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Used for current limiting in AC circuits.
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Essential in filtering and phase-shifting applications.

❌ Disadvantages / Limitations

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Introduces lag which requires power factor correction in large industrial systems.
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Reactance varies linearly with frequency.

🛠️ Applications / Uses

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Induction motor windings.
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AC chokes and ballast circuits.
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Frequency-dependent filters.

📄 Additional Information

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Option B ( $90°$ ) occurs only for an ideal inductor with zero resistance.
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Option A ( $0°$ ) occurs only for a pure resistor with zero inductance.

📊 Diagram / Illustration

✅

C is correct — The phase angle $\phi$ in an RL series circuit is always strictly between $0°$ and $90°$ because the circuit contains both resistive and inductive components.

Core Concepts Used

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Phasor Algebra Inductive Reactance Impedance Triangle

💡 EXAM TIP

Always verify if the inductor is assumed to be 'ideal' (pure) or 'practical' (has internal resistance); practical inductors always behave like an RL series circuit.

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