Question

Draw phasor diagram for a series LCR circuit with alternating voltage source, determine the expression for the impedance of the circuit.

Answer 1

Impedance of the RLC circuit as seen in the phasor diagram, can be found as

$Z=\frac{V}{I}$

$=\frac{\sqrt{(IR{)}^2+I^2(X_L-X_C{)}^2}}{I}$

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

$=\sqrt{R^2+(\omega L-\frac{1}{\omega C}{)}^2}$