Solution:
- The number of nodes is 4.
- We will number the nodes as shown to the right.
- We will choose node 4 as the reference node and assign it a voltage of zero.
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Write down Kirchoff’s Current Law for each node. Call V1
the voltage at node 1, V
2 the voltage at node 2,
V3 the voltage at node 3, and remember that
V4 = 0.
The result is the following system of equations:
The first equation results from KCL applied at node 1, the second equation results from KCL applied at node 2 and the third equation results from KCL applied at node 3. Collecting terms this becomes:
This form for the system of equations could have been gotten immediately by using the inspection method.
-
Solving the system of equations using Gaussian elimination or some other method gives the following voltages:
V1 = 1731 volts, V2 = 548 volts and V3 = 1937 volts
