Title: Node analysis example

Determine the three node voltages for the circuit shown below.

[Image: Circuit]

[Image: given currents]

[Image: given resistance]

First, we apply KCL at node a. In the schematic drawing, the reference direction of the currents is shown.

[Image: KCL node a]

[Image: Node a equation]

Next, we apply KCL at node b. Again, the reference direction of the currents is shown in the drawing below.

[Image: KCL node a]

[Image: Node a equation]

For the third equation, we apply KCL at node c. Again, in the schematic drawing, the reference direction of the currents is shown.

[Image: KCL node c]

[Image: Node c equation]

Now, we have set up a system of equations which describe the circuit.

[Image: Circuit]

[Image: System of equations]

With the help of conductance, we can simply the set of equations.

From the previous slide we have:

[Image: System of equations]

[Image: Circuit]

[Image: arrow]

[Image: System of equations with conductance]

We will now rearrange the equations.

From the previous slide:

[Image: node analysis example]

[Image: Circuit]

[Image: arrow]

[Image: System of equations rearranged]

The values for the currents and resistances will be inserted in the next step.

From the previous slide:

Given:

[Image: System of equations rearranged]

[Image: given currents]

[Image: given resistance]

[Image: arrow]

[Image: equations values]

[Image: arrow]

We can now transform the system of equations into matrix form and then solve it for v.

From the previous slide:

[Image: Circuit]

[Image: arrow]

[Image: Matrix form]

[Image: arrow]

[Image: Result]