# Nodal analysis question help?

#### Mgoo45

Joined Aug 29, 2018
5

#### 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
26,060

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?

#### Mgoo45

Joined Aug 29, 2018
5

#### Mgoo45

Joined Aug 29, 2018
5
So currently I have come up with these equations

#### MrAl

Joined Jun 17, 2014
7,756
Hi,

Did you write (15-C)/1k ?
I dont think you can do that i think you have to write (A-C)/1k for that current because you dont know what A is yet.

#### Mgoo45

Joined Aug 29, 2018
5
Hi,

Did you write (15-C)/1k ?
I dont think you can do that i think you have to write (A-C)/1k for that current because you dont know what A is yet.
Is A an essential Node though?

#### MrAl

Joined Jun 17, 2014
7,756
Is A an essential Node though?
Hi,

Well it depends on what you are calculating, and it looks like you need to calculate the node A too right?

#### WBahn

Joined Mar 31, 2012
26,060
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
26,060
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
7,756
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