Problem 1-10: Solving by Nodal Analysis – Circuit with Four Nodes

Let’s use nodal analysis to solve this circuit and determine .

Solution
I. Identify all nodes in the circuit. There are four nodes in the circuit, as indicated below

II. Select a reference node. Let’s choose the bottom node as the reference (ground) node, since all nodes have an equal number of elements connected to them.

III. Assign variables for unknown node voltages. We’ll label the remaining three nodes as ( V_1 ), ( V_2 ), and ( V_3 ), as shown above.

IV. Incorporate dependent sources. There are no dependent sources in this circuit.

V. Apply Kirchhoff’s Current Law (KCL).

For node ( V_1 ):

For node ( V_2 ):

For node ( V_3 ):

VI. Handle super-nodes.
There is no super-node in this circuit.

VII. Solve the System of Equations
Solving these equations, we get:

VIII. Determine Additional Variables.
Now, to find ( V_a ), we can apply Kirchhoff’s Voltage Law (KVL) around the loop shown below:

Download the Circuit File

To download the LTspice circuit file for your own simulations, click the link below.Please remember to unzip the file after downloading to access the .asc file for your simulations:

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