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Answer :
In an LRC circuit, resonance occurs when the impedance of the circuit is purely due to the combination of the inductance (L) and capacitance (C), not just the resistance (R) of the resistor. Hence, the given statement is false.
Resonance in an LRC (inductor-resistor-capacitor) circuit occurs when the frequency of the input signal matches the natural frequency of the circuit, resulting in maximum current and minimum impedance. At resonance, the reactive components (inductive and capacitive) cancel each other out, leaving only the resistance in the circuit. However, this does not mean that the impedance is purely due to the resistance of the resistor only.
The impedance of an LRC circuit is given by [tex]Z = \sqrt{(\text{R}^2) + (\text{X}_{L}- X_{C})^2[/tex] where Z represents impedance, R represents resistance, [tex]\text{X}_{\text{L}[/tex] represents inductive reactance, and [tex]\text{X}_{\text{C}[/tex] represents capacitive reactance. At resonance, [tex]\text{X}_{\text{L }} =\ \text{X}_{\text{C}}[/tex], which results in the minimum impedance, but the impedance is still determined by both the resistance and the reactances.
Therefore, in an LRC circuit, resonance occurs when the impedance is minimum and the reactive components cancel each other, but the impedance is not purely due to the resistance of the resistor alone.
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