1. Node - Voltage Method
ECE 201 Circuit Theory I

2. There are 3 “essential” nodes.
Identify the nodes.
There are 3 “essential” nodes.
Node 0 is the “ground” or “reference” node where the voltage is equal to zero.
Therefore there will be 2, or (ne – 1) node-voltage equations.
ECE 201 Circuit Theory I

3. Identify the node voltages
The node voltage is the voltage rise from the reference node (0) to a non-reference node (1 or 2).
Label the voltages as v1 and v2.
ECE 201 Circuit Theory I

4. Write KCL at each non-reference node.
Consider the current to be positive if it is leaving the node.
Accept the given directions of any current sources.
ECE 201 Circuit Theory I

5. ECE 201 Circuit Theory I

6. Solving for the voltages yields, V1 = 9.09 volts V2 = 10.91 volts
With polarities as assigned
ECE 201 Circuit Theory I