Nodal analysis question help?

Thread Starter

Mgoo45

Joined Aug 29, 2018
5
I would like to see a worked example just to check my working is correct. Now im aware that I have to find the current at the node C, but im just unsure how I calculate the voltage from Vcb as the question asks and Vdg.
 

WBahn

Joined Mar 31, 2012
24,853
How about showing your working and we will help you determine if, and where, there are any issues?

The notion of finding the current at a node is poorly defined. In the case of Node C, you have three branches connecting there and so, in general, you have three different currents. Which one is "the" current "at" Node C?

How many essential nodes do you have?

Which ones are they?

What is your best attempt at the node equation for each?
 

WBahn

Joined Mar 31, 2012
24,853
You are getting really sloppy and making a bunch of mistakes.

You also aren't applying Nodal Analysis correctly.

You are applying KCL in terms of branch currents and then sorta transforming them into node equations.

Nodal Analysis is the systematic application of KCL to write the node equations directly in terms of the node voltages. To apply it you sum the current leaving each node and set it to zero.

So, for instance, the node equation at Node F would be

\(\frac{V_F \; - \; V_C}{1 \; k\Omega} \; + \; \frac{V_F \; - \; V_G}{1 \; k\Omega} \; + \; \frac{V_F \; - \; V_G}{1 \; k\Omega} \; = \; 0\)

With a bit of practice, you will be able to write the equations in a form that let's you directly pull the coefficients you need to set up the matrix equations to solve the problem.

The two glaring mistakes you are making are

1) Assuming that because Node A is connected to the positive terminal of a 15 V supply that the voltage at Node A is 15 V. That would only be true if the voltage at Node B is zero.

2) Ignoring the polarity of the voltage at Node G.
 

WBahn

Joined Mar 31, 2012
24,853
Hi,

Well it depends on what you are calculating, and it looks like you need to calculate the node A too right?
Whether a node is an essential node has nothing to do with what you are calculating. An essential node is any node that has more than two branches connected to it. This problem has four essential nodes. Since you get to arbitrarily pick the voltage on one node, you need to write node equations for the other three (thus matching the number of mesh equations you would need to write).
 

MrAl

Joined Jun 17, 2014
6,621
Whether a node is an essential node has nothing to do with what you are calculating. An essential node is any node that has more than two branches connected to it. This problem has four essential nodes. Since you get to arbitrarily pick the voltage on one node, you need to write node equations for the other three (thus matching the number of mesh equations you would need to write).
Hi,

Sorry, i was talking a little more generally. Perhaps too general now that i think about it :)
 
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