Solving a Node Method Exercise - Help Needed

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In summary, the person is trying to solve an exercise on the node method but they are not quite sure if the equations are right. They were hoping if someone could give them a hand. The person has written down the equations and they are: (v1-50)/80 + (v1-v0)/40=0 (v2-v1)/40 + v2/200 + v2/800 -0,75=0. The person then asks if this is correct and is told that it is almost correct, but in Equation 2 they need to also account for the current flowing through the 800 Ohm resistor. Thanks for the help!
  • #1
esmeco
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I'm trying to solve an exercise on the node method but I'm not quite sure if the equations for the node tensions are right,so I was hoping if someone could give me a hand...Here are the node equations:

Node 1: v1/50 + (v1-50)/80 + (v1-v0)/40=0
Node 2: v0/200 + (v0-v1)/40 + (v0-50)/800 - 0,75=0

The link for the exercise is:
http://i75.photobucket.com/albums/i281/esmeco/nodemethod.jpg [Broken]


Thanks in advance for the help!
 
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  • #2
Not quite right. Call the voltage to ground at node 2 "V2" and try again. Vo as labelled is not V2. Vo is the voltage across the top resistor, not to ground.
 
  • #3
Hummm...I guess I'm not understanding quite well what you are saying...Could you or someone help me correct my equations?
 
  • #4
So...V0 would be something like: v0=(v2-v1)/800 ?
 
  • #5
esmeco said:
So...V0 would be something like: v0=(v2-v1)/800 ?
No, don't confuse currents and voltages. The node equations that you wrote originally were to use the fact that the sum of all currents out of each node must be zero. That's why each term is a voltage difference divided by the resistance between the voltages. Vo is just V2-50V.

Just go ahead and re-write the equations one more time using V2 as a term. Don't worry about Vo for now. In the end you will have V2, and that's enough to solve for Vo.
 
  • #6
Thanks!I wasn't attending to the fact that it was the voltage what we wanted to know,I thoughtthe current instead...I think I'm getting it now...
So,the equations should be something like:

Eq. 1:(v1-50)/80 + v1/50 + (v1-v2)/40=0
Eq. 2: (v2-v1)/40 + v2/200 + v2/800 -0,75=0

Is this right?
 
  • #7
Almost, but in Equation 2, you need to also account for the current flowing through the 800 Ohm resistor up on top. Add that current out of node 2 into Equation 2, and then you can solve for V1 and V2, which gives you Vo.
 
  • #8
But,Isn't that current flowing through the 800 ohm resistor given by v2/800?
 
  • #9
No. What is the voltage on the left side of the 800 Ohm resistor? It's not zero. So the current isn't (V2-0)/800.
 
  • #10
I got it...The current is (V2-50)/800.Thanks for the help!
 

1. How do I approach solving a node method exercise?

Solving a node method exercise involves breaking down the problem into smaller steps and then systematically solving each step. First, identify the nodes in the problem and assign unknown variables to each one. Then, use the given equations to create a system of equations. Finally, use algebraic methods to solve for the unknown variables.

2. What is the purpose of using a node method to solve a problem?

A node method, also known as the nodal analysis, is a systematic approach to solving electrical circuits. It allows for a more organized and efficient way of solving complex circuits by breaking them down into smaller steps. This method also helps to minimize errors and allows for easy verification of the solution.

3. What are some common mistakes to avoid while using the node method?

One common mistake is not identifying all the nodes in the circuit. This can lead to incorrect equations and ultimately an incorrect solution. Another mistake is not properly labeling the polarities of the voltage sources and current sources. This can lead to incorrect signs in the equations and therefore an incorrect solution.

4. How can I check if my solution to a node method exercise is correct?

You can check your solution by substituting the values back into the original equations and ensuring they satisfy the equations. Additionally, you can use Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL) to verify the solution. KCL states that the sum of currents entering a node must equal the sum of currents leaving the node. KVL states that the sum of voltage drops in a closed loop must equal the sum of voltage sources in that loop.

5. Are there any alternative methods for solving electrical circuits besides the node method?

Yes, there are other methods such as the mesh analysis and the superposition method. The mesh analysis involves dividing the circuit into smaller loops and using Ohm's Law and Kirchhoff's Voltage Law to solve for the unknown variables. The superposition method involves breaking down the circuit into smaller parts and solving for the unknown variables by considering one source at a time while the others are turned off. Each method has its own advantages and may be more suitable for certain types of circuits.

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