Problem 1-11: Solving a Circuit with Three Nodes by the Nodal Analysis

Solve the circuit using nodal analysis and determine the power of I_{s_1}.


Solution
I. Identify all nodes in the circuit. The circuit contains 3 nodes, as illustrated below.

II. Select a reference node. Label this node with the reference (ground) symbol.

In this circuit, two nodes are connected to the voltage source, making them suitable candidates for the reference node. We will choose the node connected to the negative terminal of the voltage source, which allows us to directly relate the voltage of the other node to the voltage source.

wp_stand_ad_camp_2

III. Assign variables for unknown node voltages. We label the remaining two nodes as V_1 and V_2, 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, since it is connected to the reference node via a voltage source, we can directly state that:

V_1 = V_{s_1} = 10 \, \text{V}.

For node V_2, we can write the KCL equation as follows:

I_{s_1} + \frac{V_2}{R_2} + \frac{V_2 - V_1}{R_4} = 0.

Substituting V_1 = 10 \, \text{V} and I_{s_1} = -2 \text{A}, R_2 = 4 \, \Omega, R_4 = 1 \, \Omega:

-2 + \frac{V_2}{4} + \frac{V_2 - 10}{1} = 0.

Solving this equation yields:

V_2 = 9.6 \, \text{V}.

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

VII. Solve the System of Equations.
All node voltages already determined.

VIII. Determine Additional Variables. Calculate the power of I_{s_1}.

The power supplied by the current source I_{s_1} can be calculated as:

P_{Is_1} = Is_1 \times V_2 =  - 19.2 \text{W,  supplying}.

LTspice Analysis

Below is the LTspice schematic for the circuit.

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:

Comments

8 responses to “Problem 1-11: Solving a Circuit with Three Nodes by the Nodal Analysis”

  1. monika Avatar

    I need more number of problems regarding to nodal ananlysis

    1. Dr. Yaz Z. Li Avatar

      There are some other solved problems about nodal analysis. Search or click on the tag.

  2. ignetius Avatar
    ignetius

    hy,,, am a little bit confuse about this nodal anaysis

  3. malik aslam Avatar

    plz tell me about the node and i m confused how much nodes can be made
    [img]334[/img]

  4. malik aslam Avatar

    plz tel me about the node and i m confused about the nodals number in the above image

  5. Faraz Avatar
    Faraz

    why aren’t the resistors R1 and R3 contributing in this nodal analysis?

  6. Opeyemi Avatar
    Opeyemi

    I’m confused about this nodal analysis

  7. Zeeshan Yaqoob Avatar

    I need more number of dificult problems related to Nodal Analysis

Leave a Reply

Your email address will not be published. Required fields are marked *