​ An ac source of voltage is connected to a series combination of LCR circuit. ​

Question

An ac source of voltage \(v = v_m \space sin\omega t\) 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.

Answer 1

Let an AC voltage source of the form v = V_msin\(\omega\)t be connected to an LCR circuit consisting of an inductor (L), a capacitor (C) and a resistor (R) in series

The total impedance Z of the circuit is given by

Phasor Diagram

(Phasor diagram consists of voltage phasors for resistor, inductor, and capacitor. Voltage across R is in phase with current, across L leads current by 90°, and across C lags current by 90°)