Nodal analysis with voltage source

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Discussion Overview

The discussion revolves around the application of nodal analysis to calculate voltages Va and Vb, as well as currents IE1 and IE2 in a circuit with voltage sources. The focus is on resolving issues encountered during the analysis without using source conversions.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • The original poster presents equations derived from their analysis but expresses uncertainty about their correctness, stating that their results do not match expected values for Va and Vb.
  • One participant questions the placement of the voltages Va and Vb in the circuit, suggesting that this may be a source of confusion.
  • Another participant clarifies the voltage across a resistor and prompts the original poster to reassess the voltage difference across another component in the circuit.
  • Further clarification is provided regarding the inclusion of voltage sources in the equations, highlighting potential omissions in the original equations presented by the poster.
  • The original poster later indicates that they have resolved their issues with the analysis.

Areas of Agreement / Disagreement

Participants engage in clarifying the original poster's approach and identifying potential errors, but there is no consensus on the correctness of the initial equations or the final results. The discussion remains somewhat unresolved as the original poster's final solution is not shared in detail.

Contextual Notes

There are indications of missing assumptions regarding the circuit configuration and the treatment of voltage sources, which may affect the accuracy of the equations presented. The discussion also highlights the importance of clarity in mathematical expressions.

Stevenfred
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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
another exam one.jpg
another exam one.jpg


 
Last edited by a moderator:
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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.
 
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.
 
The voltage on one side of R1 is Va. The voltage on the other side of R1 is -10V. The voltage difference gives you the voltage across R1, and the voltage difference is Va - (-10).

Now, try again to find the voltage difference across R3.
 
Stevenfred said:
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:
Fig1.png

Stevenfred said:
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 :smile:
 
Thank you all for your help, I figured it out .:smile:
 

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