Question

Inductance $L$, capacitor $C$ and resistor $R$ are joined in series with an alternating voltage source $V=v_0\sin \omega t$. Find the formula of impedance and phase angle, drawing vector diagram of the circuit.

Answer 1

From Fig.$2$

$V=i\sqrt{R^2-(X_L-X_C{)}^2}$ equation $1$

$V=iZ$ equation $2$

Comparing $1$ and $2$

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

Phase angle $\varphi ={\tan }^{-1}\frac{X_L-X_C}{R}={\cos }^{-1}\frac{R}{Z}$