Node Voltage Analysis: Solving VA & VB

[kdeucesd]

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?

 

[kdeucesd]

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

 

[AlephZero]

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 ...

 

[kdeucesd]

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.

 

[alphy]

Nodal analysis is a powerful tool for analyzing complex electrical circuits, but it can be challenging to set up equations for nodes that are not directly connected to the reference node. In this case, it sounds like VA and VB are not directly connected to the reference node, which can make it difficult to determine their voltages using nodal analysis.

One approach you could take is to use Kirchhoff's Voltage Law (KVL) to create a loop equation that includes VA and VB. This equation would include the voltage source and resistor between VA and the reference node, as well as any other components in the loop. You can then use the other known voltages (VC and VD) and the KVL equation to solve for the voltage at VA and VB.

Another approach is to use the concept of supernodes. A supernode is a combination of two or more nodes that are not connected by any elements, but have a voltage source between them. By treating these nodes as a single entity, you can simplify the circuit and create equations that include the voltage source and resistor between VA and VB. This can make it easier to solve for the voltages at these nodes.

It is also important to double check your circuit and measurements to ensure they are accurate. Sometimes discrepancies can occur due to faulty components or incorrect connections.

Overall, nodal analysis can be a complex process, but with careful consideration and the use of tools like KVL and supernodes, you can successfully determine the voltages at VA and VB. I hope this helps point you in the right direction.