Determine the power of each source after solving the circuit by the nodal analysis.
I. Identify all nodes in the circuit.
The circuit has 6 nodes as indicated below.
II. Select a reference node. Label it with the reference (ground) symbol.
The bottom left node is connected to 4 nodes while the other ones are connected to three or less elements. Therefore, we select it as the reference node of the circuit.
III. Assign a variable for each node whose voltage is unknown.
We label the remaining nodes as shown above. is connected to the reference node through a voltage source. Therefore, it is equal to the voltage of the voltage source: .
IV. If there are dependent sources in the circuit, write down equations that express their values in terms of node voltages.
There is no dependent voltage source here.
V. Write down a KCL equation for each node.
Nodes of and are connected by a voltage source. Therefore, they form a supernode. The negative terminal of the voltage source is connected to and the positive terminal is connected to . Thus, This can also be verified by a KVL around the loop which starts from the reference node, jumps to the node of with (the reference is always assumed to be the negative terminal of node voltages), passes through the voltage source by and returns back to the reference node from as
Supernode of & :
Node of :
Node of :
Hence, we have the following system of equations:
This system of equations can be solved by any preferred method such as elimination, row reduction, Cramer’s rule or other methods. We use the Cramer’s rule here:
All node voltages are found. The current of the source is the current of the resistor, which is The current direction shosen such that the current enters from the positive terminal of the voltage source. This is only to comply with the passive sign convention. Now that we have the source current, its power can be easily calculated:
The current of the source equals to the summation of the currents of and resistors. Therefore,
The voltage across the current source is . Therefore,
The PSpice simulation result is indicated below. The PSpice schematics can be downloaded from http://www.solved-problems.com/download/1-22.zip.