• Learn the definitions of the terms for describing circuits. Know the difference between nodes and essential nodes, branches and essential branches.
• For a network with n nodes and b branches, know the number of Kirchhoff's Voltage Law and the number of Kirchhoff's Current Law independent equations required to describe the circuit.
• Know how to apply Kirchhoff's current law to write the node-voltage equations for a network consisting of independent sources and resistors.
• Be able to modify the node-voltage equations to take accouunt of independent sources.
• Understand how to modify the node-voltage method for the case where a voltage source is connected between two essential nodes.
• Know how to use the concept of a supernode to simplify the node-voltage analysis method.

Skills: In studying the material in these sections, you should make certain that you develop the following skills:

• Write the node-voltage equations for a network consisting of independent and dependent sources and resistors using Kirchhoff's current laws.
• Solve the node-voltage equations for a network consisting of independent and dependent sources and resistors using standard algebraic methods.
• Use the node voltages to find the branch currents and the branch powers in a resistive network.

Review Questions: Test your understanding of the material in these sections by answering the following review questions:

1. Design your own three (essential) node network with three resistors and two current sources so that the node voltages are v₁ = 10 V and v₂ = 5 V.

2. Repeat the preceding example for the case where v₂ = -5 V.

3. In a network consisting of resistors and independent sources, if the values of all the resistors are doubled, what happens to the node voltages? What happens to the total power consumed by the resistors.