Solved Problems

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

Written by

Yaz

in

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


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 ):

-I_{s_2} + \frac{V_1 - V_2}{R_3} + \frac{V_1 - V_3}{R_1} = 0 \rightarrow 6V_1 - V_2 - 5V_3 = 5.

For node ( V_2 ):

I_{s_3} + \frac{V_2 - V_1}{R_3} + \frac{V_2}{R_2} = 0 \rightarrow -4V_1 + 9V_2 = -40.

For node ( V_3 ):

-I_{s_1} - I_{s_3} + \frac{V_3 - V_1}{R_1} = 0 \rightarrow V_3 - V_1 = 4.

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

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

( V_1 = 37 \, \text{V} ), ( V_2 = 12 \, \text{V} ), and ( V_3 = 41 \, \text{V} ).

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

-V_1 - V_a + V_2 = 0 \rightarrow V_a = -25 \, \text{V}.

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:

Nodal Analysis – Four-Node Circuit.ascDownload

Comments

3 responses to “Problem 1-10: Solving by Nodal Analysis – Circuit with Four Nodes”

  1. Joseph kyei baffour Avatar
    Joseph kyei baffour

    Wow.

    Reply
  2. aray Avatar
    aray

    Would it not be easier if we had taken v2 in the circuit as reference node?

    Reply
  3. hagos Avatar
    hagos

    your solution beast for eletrical engineering.

    Reply

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