Circuit Problem. Potential Difference

[sky.flower1234]

Homework Statement

Find potential difference Vab between points a and b on the figure. All resistances and emf’s are indicated, note the polarity of the batteries. What happens if the polarity of E1 is reversed (polarity of E2 kept the same) and both emfs are made equal?

Homework Equations

Okay, so you definitely need to use Kirchoff's rules here.

I also read in my text that if you want to find Vab all you do is go from point b to point a on your circuit (I'm wondering if me solution is too simple) (I did make a circuit through a program however that proves my answer.

The Attempt at a Solution

For the first part I got that Vab= -(R2(I1+I2)) (I1 and I2 come from E1 and E2)

also, I saw that with switching E2 there is no current through R2. I am not sure why this is true though, is it because a path goes through the least resistance?

 

[sky.flower1234]

So I calculated the total resistance for both emf to be 2R1+2R2, does this sound about right?

I just figured that R2 was in series for both while the 2R1 on the top was in parallel with the 2R1 on the bottom?

 

[I like Serena]

Hi sky.flower123! Let's start with the first part of your question.

Shouldn't the currents be eliminated, since they are not given?
I would assume the problem asks for Vab in terms of E1, E2, R1, and R2.Btw, hat do you mean by "total resistance"?
I think you can only talk about a "total resistance" if there is a maximum of 1 emf involved.
And anyway, the problem doesn't ask for a total resistance, does it?As for the second part of your question.
If the emf's are made equal, what would happen to the ratio of the currents?

 

[sky.flower1234]

Hey!

When I say total resistance I mean of all the resistance combined in the circuit to help me find I1+I2 (this is including both E1 and E2)

I changed up my formula to say this:

-(R2*(E1+E2/2R1+2R2)

for the second part of the question I guess the ration of my currents would be -1:1? This means they would cancel out?

 

[I like Serena]

Hmm... that looks...

Right for all parts!

(Although I would expect the direction of Vab to be the other way around, but if your book says so, then I guess it's okay.)

 

[sky.flower1234]

I was mainly just going off of how my book says to go from point B to point A and that Vab=Va-Vb. Plus using Kirchoff's rules I figured that I am going in the way of the current across a resistor so then my change in potential would be negative?

 

[I like Serena]

You're quite right.
I just expected: Vab = Vb - Va.
But as I said, if your book says it's the other way around, that's what it is for you! :)