Consider the following statements:1.In a series RLC circuit at resonance, impedance is purely resistive.2.Voltage across L and C individually can be greater than source voltage.3.Power consumed at resonance is zero.Which of the above statements is/are correct?

Correct Answer: A - 1 and 2 only

Quick Concept Explanation

Electrical resonance occurs when the net reactive effect cancels. For a series RLC circuit, XL=XC at resonance, so the impedance is purely resistive and minimum, current is maximum, and power factor is unity. Key relation: ω₀=1/√(LC); f₀=1/(2π√LC); at resonance XL=XC.

Exam focus: Series resonance: Z minimum, I maximum. Parallel resonance: input Z maximum (ideal case). Common trap: Reactive voltages can be large even though net reactive voltage is zero.

Statement-wise Verification

• Statement 1 - Correct.
  In a series RLC circuit at resonance, impedance is purely resistive.
  For a series RLC circuit, XL=XC at resonance, so the impedance is purely resistive and minimum, current is maximum, and power factor is unity.
• Statement 2 - Correct.
  Voltage across L and C individually can be greater than source voltage.
  The individual inductor and capacitor voltages may be much larger than the source voltage because of voltage magnification.
• Statement 3 - Incorrect.
  Power consumed at resonance is zero.
  In series resonance the reactive powers cancel but the resistor still consumes real power; with fixed supply the current and real power are actually at their maximum

Core Concept

Electrical resonance occurs when the net reactive effect cancels. For a series RLC circuit, XL=XC at resonance, so the impedance is purely resistive and minimum, current is maximum, and power factor is unity. The individual inductor and capacitor voltages may be much larger than the source voltage because of voltage magnification. In an ideal parallel resonant circuit the input impedance is high, not minimum.

Formula / Key Relationship

ω₀=1/√(LC); f₀=1/(2π√LC); at resonance XL=XC.

Why the Other Options Are Wrong

Option B is incorrect because it omits correct statement(s) 1. Option C is incorrect because it omits correct statement(s) 2. Option D is incorrect because it includes incorrect statement(s) 3.

Exam Shortcut / Approach

Series resonance: Z minimum, I maximum. Parallel resonance: input Z maximum (ideal case).

Common Mistake

Reactive voltages can be large even though net reactive voltage is zero.

Quick Revision

Series RLC Resonance is linked with Series Resonance, RLC Circuits and Network Theory. Series resonance: Z minimum, I maximum. Parallel resonance: input Z maximum (ideal case).