Question

Explain the impedence in LCR circuit.

Answer 1

The impedance of LCR cirquit in Cartesian form is:

$Z=R+j\omega L+\frac {1}{j\omega C}=R+j(\omega L-\frac {1}{\omega C}).$

The real part of impedance (R) is called resistive impedance, the imaginery part is reactive impedance, which consists of inductive ($\omega L$) and capasitive ($\frac{1}{\omega C}$) components.

The impedance of LCR cirquit can also be expressed in the polar form:

$Z=|Z|e^{jarg(Z)}$ ,

where |Z| - the magnitude of impedanse, which represents the ratio of the voltage difference amplitude to the current amplitude and equals:

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

arg(Z) - the argument of impedanse, which represents the  phase difference between voltage and current and equals:

$arg(Z)=arctan\frac{\omega L-\frac{1}{\omega C}}{R}.$