Question

Derive an expression for impedence and current in the series $LCR$ circuit using phasor diagram

Answer 1

Let, $V=V_{0}sin\omega t$

Where, $X_L=$ Inductive reactant.

$X_C=$ Capacitive reactant

and $i=$ Current in circuit

Impedance $Z$ is

$Z=\sqrt{R^2+({X_L-X_C)}^2}$

From Phasor diagram,

$i=\frac{V_0}{Z}sin(\omega t-\varphi )$

where $\varphi =$ Phase difference.

$\varphi ={tan}^{-1}\left(\frac{X_L-X_C}{R}\right)$