In a Series LCR Circuit Operating at the Resonant Frequency, the Current

Answer: Option C. Is in phase with the applied voltage

In a series LCR circuit operating at the resonant frequency, the current is in phase with the applied voltage.

Solution

In a series LCR circuit, at resonance 

X_L=X_C

The impedance of the circuit becomes entirely resistive. For a resistive circuit, the current is in phases with the voltage.

The voltage across the inductor at resonance V_L=jQV

The voltage across the inductor at resonance V_C =-jQV

Where Q is the quality factor of the circuit.

V = V_R+V_L+V_C = V_R+jQV-jQV = V_R

The complete source voltage appears across the resistor only. 

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