AC Circuit Analysis

Impedance

Impedance, represented by the symbol $Z$, is a measure of the opposition to electrical flow. It is measured in ohms $\text{ohm}$.

Resources

• Impedance by the Organic Chemistry Tutor

Difference between Resistance and Impedance?

Resistance is measured for DC circuits. Impedance is a more complex concept that includes resistance, but also the Reactance.

Khan Academy

I saw this Khan academy video where they use this formula, which is the norm of Impedance. $Z=\sqrt{R^2+(X_L-X_C{)}^2}$

In general, for $R$, $L$, and $C$ combinations, the impedance is defined to be the ratio between the Voltage Phasor $\tilde{V}$ and the Current Phasor $\tilde{I}$. $Z=\frac{\tilde{V}}{\tilde{I}}$

Impedance of Resistance

$Z_R=R$ $\tilde{V}=Z_R\tilde{I}$

Impedance of Inductance

$Z_L=\frac{\tilde{V}}{\tilde{I}}=j\omega L$ $\tilde{V}=Z_L\tilde{I}$

Impedance of Capacitance

$Z_C=\frac{\tilde{V}}{\tilde{I}}=\frac{1}{j\omega C}=\frac{-j}{\omega C}$ $\tilde{V}=Z_C\tilde{I}$

Rectangular Form

Another definition of Impedance is simply combining resistance $R$ and Reactance $X$ (which is defined for both $L$ and $C$) $Z=R+jX$

Combinations of Impedance

These follow the same formula as for Resistor, but they are in terms of complex impedances instead of real resistance.

For series impedances, the formula is $Z_{eq}=Z_1+Z_2+Z_3+\dots$

For parallel impedances, the formula is $\frac{1}{Z_{eq}}=\frac{1}{Z_1}+\frac{1}{Z_2}+\frac{1}{Z_3}+\dots$

Related

• Admittance
• Series Reasonance