Correct Answer

Concept & PrincipleElectricalBasic Electrical

Option D

All of above

Quick Summary: In an RLC series circuit, resonance occurs when the inductive reactance equals the capacitive reactance, causing them to cancel each other out. This results in the circuit behaving as a purely resistive load, where impedance is minimum and current is maximum.

💡 Explanation

In an RLC series circuit, resonance occurs when the inductive reactance equals the capacitive reactance, causing them to cancel each other out. This results in the circuit behaving as a purely resistive load, where impedance is minimum and current is maximum.

🔢 Key Formulas

$X_L = 2\pi f_r L$ — Inductive Reactance

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

$Z = \sqrt{R^2 + (X_L - X_C)^2}$ — Total Impedance

$f_r = \frac{1}{2\pi\sqrt{LC}}$ — Resonant Frequency

⚙️ Working Principle

The inductive reactance $X_L = 2\pi fL$ increases with frequency, while capacitive reactance $X_C = \frac{1}{2\pi fC}$ decreases. At the resonant frequency $f_r$ , these magnitudes equalize ( $X_L = X_C$ ), nullifying the imaginary part of the impedance $Z = R + j(X_L - X_C)$ . Consequently, the total impedance $Z$ simplifies to the resistance $R$ , and the circuit power factor becomes unity.

📌 Key Points

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At resonance, the phase angle between voltage and current is zero.
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The circuit provides minimum impedance to the source at the resonant frequency.
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Voltage magnification occurs across the inductor and capacitor.
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The circuit acts as a band-pass filter configuration.

✅ Advantages

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Maximum current flow for a given voltage source
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Selectivity in radio tuning circuits

❌ Disadvantages / Limitations

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Risk of voltage breakdown due to high Q-factor
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Sensitive to frequency variations

🛠️ Applications / Uses

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Radio frequency tuning circuits
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Band-pass filter designs
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Induction heating systems

📄 Additional Information

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The Q-factor (Quality Factor) determines the sharpness of the resonance curve: $Q = \frac{1}{R}\sqrt{\frac{L}{C}}$ .
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If $X_L > X_C$ , the circuit is inductive (lagging pf); if $X_C > X_L$ , it is capacitive (leading pf).

📊 Diagram / Illustration

✅

D is correct — All listed conditions ( $Z=R$ , $X_L=X_C$ , $I=V/R$ ) define the state of resonance in an RLC series circuit.

Core Concepts Used

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Resonance Impedance Complex Reactance

💡 EXAM TIP

Always remember that resonance in series circuits leads to minimum impedance, while in parallel circuits, it leads to maximum impedance.

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