Finding emf1, R1 & R2 from a graph

[Omar FTM]

Homework Statement

Both batteries in Figure (a) are ideal. Emf 1 of battery 1 has a fixed value, but emf 2 of battery 2 can be varied between 10.0 V and 100.0 V. The plots in Figure (b) give the currents through the two batteries as a function of 2. The vertical scale is set by is = 0.48 A. You must decide which plot corresponds to which battery, but for both plots, a negative current occurs when the direction of the current through the battery is opposite the direction of that battery's emf. What are (a) emf 1, (b) resistance R1, and (c) resistance R2?

Homework Equations

1/R = I/V = slope

The Attempt at a Solution

The / plot seems the 2nd battery while the \ seems the 1st as when the 2nd battery provide more current , the 1st one will provide less current.
The slope (1/R) of the / = 1 >>> R2( of battery ) =1 , the slope of \ = 3/4 >> R1 (of battery) = 4/3.
Using the first point of each plot , At E2 = 10v , the emf1 plot (\) current = 1.2 A & the emf2 plot (/) current = -0.96 A.
Are my steps right so far ? what should I do next ?

 

[BvU]

Hi Omar,

The / plot seems the 2nd battery while the \ seems the 1st

I agree. What about the voltages where $i_1 = 0$, respectively $i_2 = 0$ ?

The slope (1/R) of the / = 1 >>> R2( of battery ) =1

I suppose >>> is $\Rightarrow$ ? Anyway: don't agree. Not about the numbers and not about $R_2$.

slope of \ = 3/4 >> R1 (of battery) = 4/3

Don't agree. Not about the numbers and not about $R_1$.

So: first fix the numbers, then the interpretation.

 

[Omar FTM]

Where i=0 , E2(2nd battery) = 40v , E2(1st battery) = 60v. ( what is the equation to turn the E2(1st battery) to E1 of the first battery ) ?
I calculated 1\R using If-Ii\Vf-Vi from the plots , R is V\I ( the inverse ).

 

[BvU]

This ring a bell for $i_2=0$ ?

Now you re-draw the diagram for $i_1 = 0$ ...

All this gives you a few equations with a few unknowns. From then on it's just math