Simple KVL question

Ok so we had this homework where we're using KVL to find voltage across components or between two nodes/terminals. At first I thought I got the right answer fairly quickly then someone else in the class worked it and got a different answer and so a group of about six of use worked on it for about an hour and still weren't 100% sure if we were getting the right answer. Our teacher hasn't been the best one either and pretty much ran through a few problems then left and didn't give us any help on this problem.

The descriptions at the top where it says for example Vsub10 means the voltage between the nodes 1 and 0.

Anyway I figured (a) by first doing this problem: Vsub12+Vsub20+Vsub01=0
so Vsub12-20-50=0 from this I got Vsub12=70V

Next I go to solve Vsub32 with the following: Vsub32+Vsub20+Vsub03=0
so Vsub32-20-30=0 from this I got that Vsub32=50V

next (b) asks for Vsub31 so if Vsub32=50V and Vsub21=-70V then Vsub31 would equal 50-70 or Vsub31=-20V.

I've attached the original problem on here too. Were we doing that right? Thanks I appreciate it.

The equation for V12 is -V10-V12+V20=0 so V12=V20-V10 and if V02=20, V20=-20 and V12=-70V

For V31.

-V30+V31+V10=0, so V31=V30-V10, V31=-50V

Tell me how do you see it, and if somehting looks wrong to you.

Oh ok I see your equations and understand that. The only thing I don't understand is how you knew which direction to go when figuring this out?

Look, you don't have any currents drawn in the circuit, but you always need them to take a polarization for the resistors, so I took the one given by the signs of the voltages given in the problem, that's how you can know it. But there have to be given the currents because they polarize the resistors or more commonly you take them as you want it. If the result for a current is negative then the current actually flows in the opposite direction.

Oh ok go it haha. Had a brain fart there for a second. Thanks I appreciate it.

You're welcome, make sure to check it with your classmates (the smartests) and your teacher.

Ok the teacher apparently posted the answers (I have already turned this assignment in I was just curious to know). She said she would post them at five but aparently just got around to it. Anyway she got:

(a) V12+V20+V01=0
V12+(-20)+(-50)=0
V12=70

and

(b) V13+V30+v01=0
V13+30+(-50)=0
V13=20

Wow now that I have the answer it makes perfect sense.... I wish I could see these things without getting so confused every time.

If she takes V20=+ and V01=+ she is violating the sign convention the same happens if she takes V30=+ and V01=+, also when they are asking you to determine any voltage they have to give you its polarity, and that's not your case. If you could simulate it you will see.

I don't really understand what you're saying but I think what she meant was at the top of the problem it states that V02=20V that means between the nodes '0' and '2' the voltage is 20V but if you were to switch the leads say the positive lead was on node 0 and the negative lead was on node 2 then you switch the leads V20 (+on2 and -on0) you get -20V.

Look, That's not what I am saying, what i'm trying to tell you is that you just can't make a mesh equation without assuming a current direction, and if the problem tells you to determine a voltage it has to give you it polarity, because how are you going to take it in you equation? is it a drop or a raise?

Your teacher's equation is wrong because she took a drop (V20) + and a raise (V01) + too. And also you don't know V12 polarity.

Yeah thats what kept confusing the class was V12 and the circle. you had no clue of their polarity. And we weren't sure which component was the supplier and which ones weren't.
We assumed that the component labeled v20 was a supplier because the positive voltage across it was from node 0 to node 2 or V02. Hmm I don't think this teacher answers emails but I'm going to try to get a hold of her and see her reasoning.

i think you are not clear in one point when you say V12 it means voltage of node 1 relative to node 2
for example you have a data V10= 50 means volate of node 1 relative to node 0. ie node 1 is at higher potential.
so another word V01= -50.

so this is what you relaly sonsider when you write the KVL.
ex: V32+V20+V03=0
means (voltage of node 3 relative to node 2) + (votage of node 2 relative to node 0) + (voltage of node 0 relative to node 3) = 0

V03= -V30= - 30. and V20= - V02 = - 20

thus V32 - 30 - 20 = 0
V32= 50

you can work out the same for all.

NOTE: ON THE SKETCH YOU HAVE WRONGLY MARKED THE POLARITY OF V20.
ITS GIVEN V02= 20 MEANS V20= -20, YOU MISSED THIS POINT.

THE CORRECT ANSWERS
a) V12=70
b) V31= -20

edit: see the attched, marking of arrow to show the direction of potential at known sources. another way to check you answer.
V12 voltage of node 1 reative to 2, so node 2 has to be the reference and just go via the known path from node 2 to node 1, when the voltage is on the same direction of arrow put it as +ve and if its oposite them put _ve sign.

here V12= +20 +50 = 70
same as V31= (go from 1 to 3) -50 + 30 = -20

Those are the answers I originally got. And the image is a direct copy of the homework page I copy and pasted it from the homework pdf. I think she shouldn't have labeled the components the same as the nodes that can create confusion.

But what you're saying is the answer is what I got at first.

if you work on the data given you will get correct answers. the marking on the home work is wrong, if its correct then you should take V20=20 not V02=20. see another way to check your answers as on my previous reply