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

By BYJU'S Exam Prep

Updated on: September 25th, 2023

In a series LCR circuit operating at the resonant frequency, the current-

1. Lags the applied voltage.
3. Is in phase with the applied voltage.
4. Is zero.

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

XL=XC

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 VL=jQV

The voltage across the inductor at resonance V=-jQV

Where Q is the quality factor of the circuit.

V = VR+VL+VC VR+jQV-jQV = VR

The complete source voltage appears across the resistor only.

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