Nodal analysis with voltage source

[Stevenfred]

Homework Statement

Use nodal analysis to calculate Va, Vb, and the currents IE1 and IE2 without using source conversions

I have tried this many, many times, and I must be missing something

Homework Equations

[/B]
The equations I came up with:

VA-10/ 1.1 + VA/1.2 +VA-VB/1.4 = 0

VB+2/1.5 + VB-VA/1.4 +.5 = 0

The Attempt at a Solution

[/B]
This results in

VA (1/1.1+1/1.2 + 1/1.4) - VB (1/1.4) = 10/1.1
-VA ( 1/ 1.4) + VB (1/1.5+1/1.4) = -1.833

when put in a matrix, I am getting the wrong answers, because VA is supposed to be -4.81 and VB is supposed to be -1.80

Thanks for your help

 

[gneill]

Hi Stevenfred, Welcome to Physics Forums!

Your diagram doesn't specify where you've chosen to put VA and VB. Can you clarify that? I suspect that you've got some issues dealing with the voltage sources in the branches, but we should start with a firm definition of the nodes.

 

[Stevenfred]

Sorry that slipped my mind, and thank you for the welcome. Node A is the left side directly under R2 and Node B is on the right under R4.

 

[NascentOxygen]

The voltage on one side of R1 is V_a. The voltage on the other side of R1 is -10V. The voltage difference gives you the voltage across R1, and the voltage difference is V_a - (-10).

Now, try again to find the voltage difference across R3.

 

[gneill]

Sorry that slipped my mind, and thank you for the welcome. Node A is the left side directly under R2 and Node B is on the right under R4.

Okay, no problem. So your circuit looks like this:

The equations I came up with:

VA-10/ 1.1 + VA/1.2 +VA-VB/1.4 = 0

VB+2/1.5 + VB-VA/1.4 +.5 = 0

For the first equation, note that the 10 V source effectively increases the potential to the reference node. That is, if you assume a current $I$ flowing from VA towards the reference node, a "KVL walk" of the branch would be: $VA - I~R1 +10 = 0$, making $I = (VA + 10)/1.1$ . You've also left out the 2 V source in the branch between VA and VB. Can you redo the first equation now?

For the second equation, I don't understand your first term. I see only the 1.5k resistor in that branch so the 2V value is a mystery, and the second term leaves out the 2 V source in the VB to VA branch. The .5 term for the current is fine though.

You should get in the habit of using parentheses to group your terms so that the order of operations is clear. VB - VA/1.4 is something quite different from (VA - VB)/1.4

 

[Stevenfred]

Thank you all for your help, I figured it out .