As disccussed in the previous section, most of the methods for the study of DC circuits can be used to study AC circuits (Ohm's law, current division, voltage division, nodal analysis, mesh analysis, superposition, Thévenin's' theorem, Norton's' theorem, and source transformation) if we perform the analysis in frequency (or complex) domain. We summarize these techniques below.

Ohm's law can be extended to AC circuits, in which case the resistor is replaced with a frequency-dependent impedance. $$\begin{equation}V=ZI\end{equation}$$ or $$\begin{equation}I=\frac{V}{Z}\end{equation}$$

Current division can be extended to AC circuits, in which case the resistors are replaced with frequency-dependent impedances. In general, if we have $n$ impedances connected in parallel and the total current going through them is $I$, the current going through impedance $Z_i$ is equal to $$\begin{equation}I_i=I\frac{\frac{1}{Z_i}}{\frac{1}{Z_1}+\frac{1}{Z_2}+...+\frac{1}{Z_n}}\end{equation}$$

Voltage division can be extended to AC circuits, in which case the resistors are replaced with frequency-dependent impedances. In general, if we have $n$ impedances connected in series and the total voltage across them is $I$, the voltage across impedance $Z_i$ is equal to $$\begin{equation}V_i=V\frac{Z_i}{Z_1+Z_2+...+Z_n}\end{equation}$$

The complex impedance of an two-port network containing resistors, inductors and capacitors can be computed in the same manner as the resistance of DC networks, provided that the the real values of the resistors are now replaced with complex values corresponding to each impedance. The same rules for the simplification of series and parallel connections that we learned for the resistive networks can be applied to calculation of the complex impedance.

The same algorithm that we used for the calculation of potentials and currents in DC circuits can now be used to compute the complex values of the potentials and currents in AC circuits. Please look at the examples provided in the Sample Solved Problems.

The superposition method can also be applied for the calculation of complex potentials and currents in AC circuits. Please look at the examples provided in the Sample Solved Problems.

The Norton and Thévenin theorems remaing valid for the calculation of complex potentials and currents in AC circuits. Please look at the examples provided in the Sample Solved Problems.

• AC nodal analysis
  AC circuit without dependent sources or supernodes in complex form
  AC circuit without dependent sources but with supernodes in complex form
  AC circuit with dependent sources and supernodes in complex form
  AC circuit without dependent sources or supernodes in time-domain
  AC circuit without dependent sources but with supernodes in time-domain
  AC circuit with dependent sources and supernodes in time-domain
  
• AC mesh analysis:
  AC circuit without dependent sources or supermeshes in complex form
  AC circuit without dependent sources but with supermeshes in complex form
  AC circuit with dependent sources and supermeshes in complex form
  AC circuit without dependent sources or supermeshes in time-domain
  AC circuit without dependent sources but with supermeshes in time-domain
  AC circuit with dependent sources and supermeshes in time-domain
  
• AC superposition:
  AC circuit with 2 sources in complex form
  AC circuit with 3 sources in complex form
  
• AC source transformation:
  AC circuit with 2 sources
  AC circuit with 3 sources
  
• AC Norton-Thévenin equivalent circuits:
  AC circuit with 2 loops and one independent source AC circuit with 3 loops and 2 independent sources AC circuit with 3 loops and 2 sources