Node Voltage Analysis: Solving VA & VB

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Discussion Overview

The discussion revolves around determining the node voltages VA and VB in a circuit using node voltage analysis. Participants explore different approaches to set up equations for these voltages, considering the presence of resistors and voltage sources.

Discussion Character

  • Technical explanation, Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant expresses difficulty in setting up the equation for VA due to the circuit configuration involving a resistor and a voltage source.
  • Another participant provides equations for VA and VB based on their analysis, suggesting a specific approach to nodal analysis.
  • A different participant proposes an alternative method using loop currents and KVL equations, indicating that simplification of the circuit could be beneficial.
  • One participant mentions successfully using mesh current analysis but is required to apply node voltage analysis as well.
  • There is a reference to combining resistors in the equations, suggesting that some participants are working towards simplifying their calculations.

Areas of Agreement / Disagreement

Participants present various methods and approaches to the problem, indicating that there is no consensus on a single solution or method. Multiple competing views remain regarding the best approach to analyze the circuit.

Contextual Notes

Some participants' equations depend on specific assumptions about the circuit configuration, and there may be unresolved steps in the mathematical derivations presented.

kdeucesd
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I am having a hard time trying to determine the voltage at VA and VB. I know that VC = VD = 10V. At first I thought this would be a simple setup, but I'm unsure about how to set up an equation for VA considering that there is a resistor and a voltage source between it and the reference node. I've built this circuit and made measurements with a DMM, I'm just trying to come to the same results using nodal analysis. Can anyone point me in the right direction?
 

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For VA, I have (VA - 6)/100 + (VA - 10)/800 = 0
For VB, I have (VB - 10)/320 + VB/330 = 0
For VC, I have VC = 10
 
You could solve it by using 4 loop currents and then writing the KVL equations for the 4 loops.

Or you could start by simplifying the circuit, for example replace R3 and R5 by a single resistor ...
 
Using mesh current analysis was a breeze, but I am also asked to use node voltage.

As far as your second suggestion, I combined those resistors in the equations above.
 

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