Question

An ac source of voltage \( v = v_m \sin \omega t \) is connected to a series combination of LCR circuit. Draw the phasor diagram. Using it, obtain an expression for the impedance of the circuit and the phase difference between applied voltage and the current.

Hint:

The phase difference between the voltage and current in an LCR circuit depends on the relative magnitudes of the inductive reactance (\( \omega L \)) and capacitive reactance (\( \frac{1}{\omega C} \)).

Answer 1

The impedance of the LCR circuit is given by: \[ Z = \sqrt{R^2 + \left( \omega L - \frac{1}{\omega C} \right)^2} \] where \( R \) is the resistance, \( L \) is the inductance, and \( C \) is the capacitance. The phase difference \( \phi \) between the applied voltage and the current is given by: \[ \tan \phi = \frac{\omega L - \frac{1}{\omega C}}{R} \] The current lags the voltage by the phase angle \( \phi \), which can be visualized in the phasor diagram.