Nodal Analysis for ac Circuits

Kirchhoff's current law serves as the foundation for nodal analysis of alternating current circuit steady-state conditions. The nodal and supernode for an alternating current circuit are identical to those for a direct current circuit, therefore we will not have any trouble here.
Before examining the application of the method to ac networks, the student should first review the appropriate sections on nodal analysis in Chapter 6 since the content of this section will be limited to the general conclusions of Chapter 6 (Methods-of-Analysis).
The fundamental steps are the following:
  • Determine the number of nodes within the network.
  • Pick a reference node and label each remaining node with a subscripted value of voltage: $V_1$, $V_2$, and so on.
  • Apply Kirchhoff's current law at each node except the reference. Assume that all unknown currents leave the node for each application of Kirchhoff's current law.
  • Solve the resulting equations for the nodal voltages
A few examples will refresh your memory about the content of Chapter 6 and the general approach to a nodal-analysis solution.
Example 1: Find the voltage across the inductor for the network of [Fig. 1] using nodal analysis.
Fig. 1: Example 1.
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Example 2: Write the nodal equations for the network of [Fig. 3] having a dependent current source.
Fig. 3: Example 2.
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Example 3: Apply nodal analysis to the network of [Fig. 5]. Determine the voltage $V_L$.
Fig. 5: Example 3.
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