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 \( Z \) of an LCR circuit is calculated using the formula: \[ Z = \sqrt{R^2 + \left( \omega L - \frac{1}{\omega C} \right)^2} \] Here, \( R \) denotes resistance, \( L \) represents inductance, and \( C \) signifies capacitance. The phase difference \( \phi \) between the voltage and current is determined by: \[ \tan \phi = \frac{\omega L - \frac{1}{\omega C}}{R} \] The current trails the voltage by this phase angle \( \phi \), which is visually depicted in the phasor diagram.