Ac Circuits

In a series LCR circuit: - Resonance occurs when the inductive reactance equals the capacitive reactance, i.e., .
- This implies: At this frequency: - The net reactance , so the impedance (purely resistive).
- Hence, the circuit behaves like a pure resistive circuit at resonance.
Therefore: - Assertion is true.
- Reason is also true.
- And Reason correctly explains the Assertion.
Final answer: Option (A)

Given data: - Resistor - Inductor - Capacitor - Source voltage: The angular frequency of the AC source is: Step 1: Calculate the rms voltage of the source The peak voltage is , so the rms voltage is given by: Step 2: Find the impedance of the circuit The impedance of the series circuit is given by: where is the inductive reactance and is the capacitive reactance. The inductive reactance is: The capacitive reactance is: Thus, the total impedance is: Step 3: Calculate the current in the circuit The current in the circuit is: Step 4: Calculate the rms voltages across each element - Rms voltage across the resistor: - Rms voltage across the inductor: - Rms voltage across the capacitor: Step 5: Explanation of the algebraic sum The algebraic sum of the individual voltages across the resistor, inductor, and capacitor is greater than the rms voltage of the source because the voltages are not in phase with each other. In an AC circuit with reactive elements (inductor and capacitor), the voltages across the inductor and capacitor are 180° out of phase with each other, leading to their individual voltages adding up vectorially. The total voltage across the components is the phasor sum, not the simple arithmetic sum, which results in a larger total voltage than the rms voltage of the source.