Mesh and Nodal Analysis

Discussion in 'Homework Help' started by majdi, Oct 23, 2013.

1. majdi Thread Starter New Member

Jun 22, 2011
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What 5vx mean?

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2. The Electrician AAC Fanatic!

Oct 9, 2007
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Along the left edge of your network you will see a symbol Vx next to the 5Ω resistor. The component you have outlined in red is a "dependent current source", whose output current is equal to the 5 times the voltage across the 5Ω resistor.

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3. majdi Thread Starter New Member

Jun 22, 2011
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I dont know how to start with this circuit to find i0 with mesh and nodal.. 3 hour wasted. Should i used source transformation first?

4. The Electrician AAC Fanatic!

Oct 9, 2007
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I see 3 meshes. Add some more red to the diagram, showing 3 mesh currents circulating in each mesh, label the currents I1, I2 and I3. Then show an attempt at writing the 3 mesh equations.

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5. shteii01 AAC Fanatic!

Feb 19, 2010
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Do you have a textbook?

6. WBahn Moderator

Mar 31, 2012
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Of course, I have no idea what it means for a current to be five times a voltage. That's like saying that my car's fuel economy is twice my electric bill. Huh???

The "5 v_x"' should be "5A/V v_x". Then it becomes a lot more clear. The current source will put out 5 amperes of current for every volt measured across v_x.

This circuit looks like it is expecting you to use the concepts of a supermesh or a supernode. That, in turn, implies that you have worked with simpler circuits and learned how to deal with dependent sources. If necessary, go back and review that material.

Remember that mesh current analysis is nothing more than a formalized way to sytematically apply KVL to the loops in a circuit. If, when developing the KVL equations, you don't know how to express the voltage across a particular component, just assign a symbolic voltage to it, say v12 (with an indicated polarity), and use that in your equation. In doing so, you have added another unknown, but that just means you will need to come up with an additional equation based on the constraints in the relationships between the mesh currents.

Take your best shot and we can then start a focused discussion from that point.

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7. majdi Thread Starter New Member

Jun 22, 2011
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Am i doing good here? Im refer to my pdf note, if there no dependent current source example for supermesh. Correct me if im doing wrong for equation.

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8. WBahn Moderator

Mar 31, 2012
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In your first equation, consider the following:

First, look at the diagram and answer the following: If i1 turned out to be 0A, what would i2 have to be?

Now look at your first equation and answer the same question?

Do the two answers agree? If not, you've got a problem.

In the diagram on the right, why have you removed the current source? If you do that, then you force i2 and i3 to be equal. But there is no such constraint. The current source is still there, you are just summing the voltage drops around a loop that encompasses more than one mesh. That's all.

In your second equation you are not being very consistent. Notice in the third equation you have a -12V due to the voltage source as you go from negative to positive along i3. But in the second equation you have -12V from the same source as you go from positive to negative along i1. Make up your mind whether you are going to sum up voltage drops around a mesh or voltage gains around a mesh. If you mix them, you will almost certainly make hard to find errors at some point.

In that second equation, where does the "-5A/12" term come from? Is that the voltage across that dependent source? Are you sure? If you look at your units carfully, I think you will find that they do not work out to volts, which they must in order to add them to the other terms in that equation.

Look at that second equation closely. is i2 the only mesh current causing a voltage drop in the 8Ω resistor?

In the third equation, is i3 the only mesh current causing a voltage drop across the 8Ω resistor?

Consider the i2 mesh current. What does it HAVE to be equal to?

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Jun 22, 2011
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10. WBahn Moderator

Mar 31, 2012
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Very good. Here are some suggestions to make your work easier to follow and grade (which always benefits you).

You need to specify what your reference node is. Remember, you get to pick any node in the circuit and call it 0V. But don't make others guess which node that is. When you say that vx=v1, that is only true IF the bottom node is 0V. But the only indication you give of that is that you didn't assign a node label to it. You really should either write 0V near that node or draw a common (or ground) symbol there.

You need to use units. Most mistakes you make will mess up the units allowing you to find and fix them quickly. But that is only possible if you track them throughout the work.

Notice that the same equation you got for the supernode could also be had by applying KCL to the bottom node.

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11. The Electrician AAC Fanatic!

Oct 9, 2007
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You have chosen your supernode incorrectly. The supernode consists of those nodes which are connected by a voltage source, namely V1 and V2.

You may say, "Then why did I get the right answer"? You got the right answer because the current injected by the 5Vx dependent source all goes to the supernode because the 12Ω and 8Ω resistors carry all the current from the dependent source, and they are connected to V1 and V2.

What would your supernode equation have been if there were another 5Ω resistor connected from V3 to ground?

Choosing your supernode to consist of all three nodes (V1, V2 and V3) just happened to give the right answer for this problem, even though V3 is not connected to V1 and V2 by a voltage source. This won't work in general.

12. WBahn Moderator

Mar 31, 2012
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In practice, what The Electrician has just suggested is very good advice. Yes, in theory you can declare a "supernode" to encompass whatever set of nodes you want. But if it encompasses N nodes (either interior or boundary), then you have to come up N-1 equations to relate them to each other. If you follow The Electrician's advice, then coming up with those relationships is very easy. Otherwise, you have to work at it a bit harder and usually end up using the same techniques you could have used with a "properly" defined supernode. This is exactly what happened in your case; your supernode encompassed three nodes, meaning that you needed to write the equation for the supernode and then two more equations that would related the three nodes to each other. One of them you did explicity by saying that V1=V2-12V. The other one you did without really realizing it when you wrote the node equation for V3. Remember that V3 was part of the supernode you defined, so it was already taken care of. By writing the node equation for it in a manner that didn't involve the supernode, you established the relationship between V3 and the other two nodes in the supernode, V1 and V2.