Confusion with Nodal Analysis w/ Sources

[RiceKernel]

Hi , I'm currently stuck on a problem that requires to be solved with nodal analysis.

I'm confused to what signs should I use when there's a voltage source in the loop.

The problem:

I already know the answer from the solutions but what I found is at V_0 :

(V0 - 60V)/12 + V0/12 + (V0 -24V)/6 = 0

This is horrendously incorrect but I can't understand why . I know current flows from higher potential to lower so if that was the case then my first term would be correct (matches solution) ; the 2nd term is also correct (V0-0V)/12 but the last term is incorrect. The correct term would be (VO - (-24V))/6 and I really don't know why? Can someone explain that to me? Even for the first term, I just got lucky by putting the correct sign but I want to know why and how does the sign vary.

Oh and if anyone wants the answer , V0= 3V. Power in resistors are easy to find once the currents and voltages are found.

Thanks,
GT

 

[Jony130]

Because 24V voltage source has a positive terminal connected to gnd and the minus terminal to 6 ohm resistor.
And this is why voltage at right side of a 6 ohm resistor is -24V ( 24 voltages lower than voltage at GND).

The reference point determines whether we have a positive or negative voltage.
See this example

 

[RiceKernel]

Does this apply regardless of the direction of the current(s) ?

 

[Jony130]

Does this apply regardless of the direction of the current(s) ?

In this case the current direction doesn't matter here. Because only the voltage source and the reference point (GND) determines the voltage polarity.
And this is why we have -24V and 60V regardless of the direction of the currents.

 

[alphy]

Hello GT,

I can understand your confusion with nodal analysis when there are voltage sources in the loop. The key thing to remember is that voltage sources are always assumed to have a fixed voltage, regardless of the direction of current flow. This means that the voltage at a node connected to a voltage source will always be the same as the voltage of the source.

In your problem, you correctly identified the currents flowing into the node connected to the voltage source as (V0-0V)/12 and (V0-24V)/6. However, for the last term, you need to consider the direction of current flow in the loop. Since current flows from higher potential to lower potential, the current flowing through the voltage source will be in the opposite direction, from -24V to V0. Therefore, the correct term would be (V0-(-24V))/6, which simplifies to (V0+24V)/6.

I hope this explanation helps you understand the sign variation in nodal analysis. It's important to keep in mind the direction of current flow and the fixed voltage of voltage sources when setting up the equations. Good luck with your problem!