Correct Answer

Concept & PrincipleElectricalBasic Electrical

Option B

$\frac{\omega L}{R}$

Quick Summary: The Quality factor (Q-factor) of a coil is a dimensionless parameter that characterizes the resonance behavior of a resonator. It is defined as the ratio of the inductive reactance of the coil to its effective resistance at a given frequency.

💡 Explanation

The Quality factor (Q-factor) of a coil is a dimensionless parameter that characterizes the resonance behavior of a resonator. It is defined as the ratio of the inductive reactance of the coil to its effective resistance at a given frequency.

🔢 Key Formulas

$Q = \frac{\omega L}{R}$ — Quality factor of an inductive coil

$Q = \frac{1}{R}\sqrt{\frac{L}{C}}$ — Quality factor at resonance for an RLC circuit

⚙️ Working Principle

In an R-L circuit, the energy stored in the magnetic field of the inductor is proportional to $\frac{1}{2}LI^2$ , while the energy dissipated per cycle is determined by the resistance $R$ . The Q-factor represents the sharpness of the resonance peak, where a higher Q implies lower energy loss relative to the energy stored, leading to a narrower bandwidth.

📌 Key Points

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Q-factor determines the selectivity of a tuned circuit.
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Higher Q-factor results in a narrower bandwidth.
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For an ideal inductor with zero resistance, Q-factor is infinite.
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Q-factor is independent of the current flowing through the coil.

✅ Advantages

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High Q-factor improves frequency selectivity in communication systems.
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Indicates efficiency of energy storage in reactive components.

❌ Disadvantages / Limitations

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Difficult to maintain high Q at very high frequencies due to skin effect and dielectric losses.
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High Q circuits are more sensitive to component tolerance and temperature drift.

🛠️ Applications / Uses

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Radio frequency (RF) tuning circuits.
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Band-pass filters in signal processing.
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Oscillator circuits requiring stable frequency output.

📄 Additional Information

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The Q factor is also defined as $2\pi \times \frac{\text{Maximum energy stored}}{\text{Energy dissipated per cycle}}$ .
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Option A ( $\omega L$ ) represents Inductive Reactance ( $X_L$ ). Option C ( $\frac{\omega L}{C}$ ) is dimensionally incorrect for Q. Option D ( $\omega LC$ ) is related to resonant frequency square.

📊 Diagram / Illustration

✅

B is correct — The Q factor is defined as the ratio of inductive reactance $\omega L$ to the ohmic resistance $R$ .

Core Concepts Used

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Inductive Reactance Resonance Energy Dissipation Selectivity

💡 EXAM TIP

Always remember that Q is a ratio of reactive power to real power; thus, it is a dimensionless quantity that measures the 'purity' of the inductor.

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