What are the Nodal equations for the circuit?

  • Engineering
  • Thread starter t_jorgic
  • Start date
  • Tags
    Circuit Nodal
In summary, the conversation discusses a problem that involves finding the value of Is given that Vo = 6V. The person is attempting to use the Nodal Method to solve the problem, but is unsure if their equations are correct. Another person points out a mistake in the second equation and explains the correct approach to solving the problem.
  • #1
t_jorgic
2
0

Homework Statement



The problem is explained in the picture. It asks to find the value of Is given that Vo = 6v.

http://img24.imageshack.us/img24/9935/circuitst.jpg

Uploaded with ImageShack.us

Homework Equations





The Attempt at a Solution


I am attempting the Nodal Method to get a system of equations which i will solve. The problem is getting those equations. I think I am missing a few equations. Heres my attempt:

There are two nodes that I have written equations for.

Va/7 + (Va - Vb)/3 = Is

(Vb-Va)/3 + Vb/2 + Vb/3 = Is

Im not sure if these equations are right or not.
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
you have two independent nodes so you only need two equations which you have. and by the looks of it you have almost perfect equations. there is one mistake though.

What is the fundamental law that you are applying when you do node analysis?
 
  • #3
The first equation is correct, but the second one isn't. You can't equate the second equation to 'Is' for two reasons. First, there's a current flowing through the 7Kohm which is equal to (Va/7k), and second, there's no current source flowing toward or out of node 'Vb'. You need to equate the second equation to zero and find the value of Va, then, substitute in the first equation to get the value of 'Is'.

Note that Vb equals 6V.
 
Last edited:

1. What are the Nodal equations?

The Nodal equations, also known as the Kirchhoff's Current Law (KCL), are a set of equations used to determine the voltage at each node in an electrical circuit. These equations are based on the conservation of charge, stating that the sum of currents entering a node must equal the sum of currents leaving the node.

2. How do you write the Nodal equations?

To write the Nodal equations, you first need to identify all the nodes in the circuit. Then, you can apply KCL at each node by writing an equation for the sum of currents entering the node and equating it to the sum of currents leaving the node. Finally, solve the set of equations simultaneously to find the voltage at each node.

3. What are the advantages of using Nodal equations?

The Nodal equations are advantageous because they can be used to analyze circuits with multiple current sources, unlike other methods such as Ohm's Law. They also provide a systematic approach to solving complex circuits, making it easier to find the voltage at each node.

4. Can the Nodal equations be used for both DC and AC circuits?

Yes, the Nodal equations can be used for both DC and AC circuits. However, for AC circuits, the equations must be written in terms of complex numbers to account for the phase difference between current and voltage.

5. What is the significance of the Nodal equations in circuit analysis?

The Nodal equations are essential in circuit analysis as they provide a mathematical model for understanding the behavior of electrical circuits. They can be used to calculate the voltage at any point in the circuit and determine the current flowing through each component, making them a fundamental tool for designing and troubleshooting circuits.

Similar threads

Help with Circuit Nodal Analysis
    • Engineering and Comp Sci Homework Help
Replies
2
Views
1K
Solve Vo: Voltage Nodal Analysis w/ KCL Equation
    • Engineering and Comp Sci Homework Help
Replies
5
Views
2K
Nodal analysis trying to find Voc
    • Engineering and Comp Sci Homework Help
Replies
2
Views
1K
Nodal analysis with voltage source
    • Engineering and Comp Sci Homework Help
Replies
5
Views
1K
Engineering How do I solve this circuit using nodal analysis?
    • Engineering and Comp Sci Homework Help
Replies
7
Views
886
AC Nodal analysis -- help please
    • Engineering and Comp Sci Homework Help
Replies
3
Views
1K
What is the Instant Centre of Rotation for a Rotating Bar?
    • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
Balancing Support Reactions: Exploring Equilibrium in Structural Analysis
    • Engineering and Comp Sci Homework Help
Replies
2
Views
1K
Engineering Solving a Circuit with Nodal Analysis
    • Engineering and Comp Sci Homework Help
Replies
6
Views
1K
Engineering Find total power in a circuit with two power supplies
    • Engineering and Comp Sci Homework Help
Replies
15
Views
3K

Hot Threads

Recent Insights

Back
Top