Impedance

• $Z=R+jX$ is the impedance (in $\Omega$)

  • $R$ is the resistance (in $\Omega$)
  • $X$ is the reactance (in $\Omega$), where:
    • $X_L=\omega L$ is the inductive reactance
    • $X_C=\frac{1}{\omega C}$ is the capacitive reactance
    • $X=X_L-X_C$
  • $|Z|=\sqrt{R^2+X^2}$ is the magnitude of impedance
  • $\tan \varphi =\frac{X}{R}$ is the phase angle

• $Y=G+jB$ is the admittance (in S, siemens)

  • $G=\frac{1}{R}$ is the conductance
  • $B$ is the susceptance, where:
    • $B_L=-\frac{1}{X_L}=-\frac{1}{\omega L}$ is the inductive susceptance
    • $B_C=\frac{1}{X_C}=\omega C$ is the capacitive susceptance
    • $B=B_C+B_L$
  • $|Y|=\sqrt{G^2+B^2}$ is the magnitude of admittance
  • $\tan \varphi =\frac{B}{G}$ is the phase angle

• $Z_{\text{series}}=Z_1+Z_2+\cdots +Z_n$

• $Z_{\text{parallel}}={\left(\frac{1}{Z_1}+\frac{1}{Z_2}+\cdots +\frac{1}{Z_n}\right)}^{-1}$