Circuit with multiple voltage sources

[dlacombe13]

Homework Statement

a. Find the voltages Va, Vb, and Vc.
b. Find the currents I1 and I2.

Homework Equations

Ohm's Law, Current Divider

The Attempt at a Solution

[/B]
My first attempt was to redraw the circuit. I know that these voltages are with respect to ground. Therefore Va to Ground is 36v. However, I know the answer to Vb is 60v and I do not understand why. I know it is probably due to a misunderstanding as to how the current flows in this circuit.

In my mind, the current from the 60v source branches out towards R3 and R1, but I have a strong feeling that is wrong. My mind also tells me that the current chooses one direction. I know in simple series circuits, if there are two voltage sources in opposing directions, the higher source will force its direction, and that is how it is chosen. How is it chosen in this case? I think this will help me better understand how to find Vb and Vc.

 

[gneill]

Node b is at +60 V because it's established by the 60 V source. Due to that voltage source that node can't be anything but 60 V with respect to the bottom end of that source, which is attached to the reference node. It's the same reasoning that you used to determine that node a is 36 V.

The potential at node c will require that you do a little circuit analysis. In particular, you have a potential divider situation formed by R3 and R4. See what you can make of that.

Your diagrams don't identify $I1$ and $I2$. Can you clarify?

 

[CWatters]

My first attempt was to redraw the circuit.

So the first circuit is the problem statement and the second one is your attempt to redraw it?

You appear to have just swapped the names of the nodes "a" and "b". You can't do that. It would mean you are trying to find the voltage on the wrong node.

 

[gneill]

You appear to have just swapped the names of the nodes "a" and "b". You can't do that. It would mean you are trying to find the voltage on the wrong node.

Ah! I missed that relabeling! Good catch.​

 

[dlacombe13]

Oops! Yes the first drawing is the original, and it is actually supposed to be node a, then b, then c from left to right. So the node placement in the redraw is actually the correct nodes, sorry. As for the currents, I forgot to draw them, but I think I can solve those once I get my confusion with these multiple voltage sources sorted out, so just forget part b.

So I kind of get it now, but I'm still a little confused. Could you explain precisely the path of the current coming from the 36v and 60v source? And realistically, am I just connecting a voltmeter from the node to the ground, and basically getting that reading as my answer?

 

[CWatters]

The currents are largely irrelevant to understanding this problem.

Voltage sources determine the voltage difference between the nodes they are connected to. So in this case Va and Vb are trival to work out by inspecting what they are connected to. Va is connected to a 36V battery and Vb a 60V battery.

V2 (60V) also determines the voltage at the left hand side of R3 because that's also node b. At this point you can simplify the circuit by deleting all parts to the left of V2.

 

[gneill]

So I kind of get it now, but I'm still a little confused. Could you explain precisely the path of the current coming from the 36v and 60v source?

See below.

And realistically, am I just connecting a voltmeter from the node to the ground, and basically getting that reading as my answer?

In essence, yes.

As for the current flow, eyeballing the various potentials I can make the following guess as to the current flows:

You'll have to do some circuit analysis to give each of the currents a value

 

[CWatters]

And realistically, am I just connecting a voltmeter from the node to the ground, and basically getting that reading as my answer?

Yes

 

[dlacombe13]

Thank you for you help guys. The thing is, I totally get that when you say node b is connect to a 60v battery, then node b with respect to ground is obviously 60v. But I am also using this problem to understand a deeper concept, even if it is largely irrelevant to determine the answer. With that said, the concept I am really trying to grasp from this circuit is, why are the directions of the currents what they are? Why is the current going CCW through the 36v battery, and why does the current split from the 60v battery and go CW to the right? If the question were instead to simply this circuit, would the 36v and the 60v combine? Why does node b only see 60v, and has nothing to do with the 36v battery? I am sorry for all the questions, I just feel like I need to know these things to really understand how circuits work.

 

[gneill]

The nodes are separated by resistances so they can be at different potentials. It's potential difference that drives current. Current flows from higher potential to lower potential (akin to water flowing down a mountainside with different potentials representing different elevations).

Potential drops occur when current flows through a resistance (Ohm's law). If there were no resistors in your circuit the two voltage sources would indeed struggle against each other -- there would be a mighty flash and smell of burnt reality as they each attempted to achieve infinite current to get their own way

A voltage source will produce any amount of current required to establish and maintain its designated potential difference. It is quite capable of sending current along multiple paths --- after all, current is driven by potential difference. Whenever a potential difference exists and there is a path to follow, current will flow. So, for example, the +60 V at node b has three paths available and so the current takes all three according to the potential difference it sees and the resistance along the way.

 

[dlacombe13]

Okay, this is definitely starting to make sense, I think. So since the 60v battery is greater than the 36v battery, the current from the 60v battery wants to move towards the lower potential (36v battery) and does this, in turn, cause the current to then go CCW through the 36v battery, as opposed to it's original polarity?

 

[gneill]

Okay, this is definitely starting to make sense, I think. So since the 60v battery is greater than the 36v battery, the current from the 60v battery wants to move towards the lower potential (36v battery) and does this, in turn, cause the current to then go CCW through the 36v battery, as opposed to it's original polarity?

Yup. In effect, the 36 V battery is going to be charging if it's an actual battery; It will be absorbing energy rather than delivering it in this case.