Consider the following statements regarding Resonance in RLC Circuit:1.In series resonance, impedance becomes minimum and current becomes maximum.2.At resonance, inductive reactance equals capacitive reactance.3.Power factor at resonance becomes unity.4.In parallel resonance, impedance becomes minimum.Which of the above statements is/are correct?

Correct Answer: C - 1, 2 and 3 only

Quick Concept Explanation

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. In an ideal parallel resonant circuit the input impedance is high, not minimum. 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 series resonance, impedance becomes minimum and current becomes maximum.
  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.
  At resonance, inductive reactance equals capacitive reactance.
  Ω₀=1/√(LC); f₀=1/(2π√LC); at resonance XL=XC.
• Statement 3 - Correct.
  Power factor at resonance becomes unity.
  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 4 - Incorrect.
  In parallel resonance, impedance becomes minimum.
  The correct principle is: 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.

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 A is incorrect because it omits correct statement(s) 1. Option B is incorrect because it includes incorrect statement(s) 4 and omits correct statement(s) 2, 3. Option D is incorrect because it includes incorrect statement(s) 4.

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