Impedance

• Resistance for AC
• Impedance $Z=\frac{\mathbf{V}}{\mathbf{I}}$ in units $\mathrm{\Omega }$
• Admittance $Y=\frac{1}{Z}=\frac{\mathbf{I}}{\mathbf{V}}$ in $\mathrm{S}$
• $Z=R+jX$
  • Where $R$ is the resistance
  • $X$ is the reactance
• $R^2+X^2$ is the magnitude, while $X$ gives the quadrant, and so the classification of the thing
  • If $X>0$, then $Z$ is inductive
  • If $X<0$, $Z$ is conductive
  • If $X=0$, $Z$ is resistive
• $Y=G+jB$
  • $G$ is conductance in $S$
  • $B$ is susceptance in $S$
• KVL equivalent is ${\mathbf{V}}_{\mathbf{1}}+{\mathbf{V}}_{\mathbf{2}}+\cdots +{\mathbf{V}}_{\mathbf{n}}=0$ around a loop
• KCL equivalent is ${\mathbf{I}}_{\mathbf{1}}+{\mathbf{I}}_{\mathbf{2}}+\cdots +{\mathbf{I}}_{\mathbf{n}}=0$ at a node
• In series, impedances sum
• In parallel, it's like parallel resisstors
• Basically every component has impedance

Inductances for Components

• When $\omega =0$
  • $Z_R=R$ does not change
  • $Z_C=\frac{1}{j\omega C}$ becomes an open circuit
  • $Z_L=j\omega L$ becomes a short circuit
• It's flipped when $\omega =\mathrm{\infty }$