The value of impedance in a series LCR circuit at resonance is

Explanation

Impedance in a Series LCR Circuit:Impedance (Z) in a series LCR circuit represents the total opposition to the flow of alternating current (AC) and is calculated as:Z = √(R² + (XL - XC)²)where:R: ResistanceXL: Inductive reactanceXC: Capacitive reactanceResonance in a Series LCR Circuit:Resonance occurs at a specific frequency (f_r) where the inductive reactance (XL) exactly cancels out the capacitive reactance (XC). Mathematically, this means:XL = XCDuring resonance, the imaginary component of the impedance equation (XL - XC) becomes zero. As a result, the square root operation in the impedance formula simplifies to:Z = √(R²)Therefore, at resonance, the impedance of the series LCR circuit reduces to:Z = RConclusion:Since resistance (R) is a positive value, the impedance of the series LCR circuit at resonance becomes minimum and equal to the resistance (R) of the circuit