Potential difference across a resistor

[palkia]

Homework Statement

Two cells of same emf E and different internal resistance r1 and r2 are connected in series to an external resistance R.The value of R for which the potential difference across the first cell is zero is given by

(A) R=r1/r2
(B)R=r1+r2
(C)R=r1-r2
(D)R=r1r2

Homework Equations

E=IR[/B]

The Attempt at a Solution

I first founded the total current in the circuit which came to be-E/R+r1+r2 then used the equation Ir1 to get the potential difference but I am not getting my answer[/B]

 

[mfb]

What did you get as answer?

What must be the voltage drop at r1 to make this scenario possible?

By the way: It is useful to put brackets around denominators to make clear what is in the denominator. is x/y+z =(x/y)+z (as it would be usually read) or x/(y+z) (what you mean here)?

 

[palkia]

Potential difference across r1is Er1/(R+r1+r2) so for zero potential difference r1=0 which looks weird

 

[haruspex]

the total current in the circuit which came to be-E/(R+r1+r2)

No, you forgot something.

 

[palkia]

2E/R+r1+r2

 

[haruspex]

2E/R+r1+r2

Right, but please use parentheses correctly.
If the PD across the first battery is zero, what current would you expect?

 

[palkia]

E=2E/(R+r1+r2) r1

But why are solving for the terminal voltage of the battery?

 

[haruspex]

E=2E/(R+r1+r2) r1

But why are solving for the terminal voltage of the battery?

I believe that equation gives the right answer.

 

[palkia]

E-Ir1

 

[haruspex]

E-Ir1

I do not see how you got that from the equation in post #7. Please show your working.

 

[palkia]

I do not see how you got that from the equation in post #7. Please show your working.

E-2 E r1 /(R+r1+r2)

 

[palkia]

So the potential difference across the interal resistor issame as terminal voltage of the battery?

 

[mfb]

So the potential difference across the interal resistor issame as terminal voltage of the battery?

Right.

 

[haruspex]

E-2 E r1 /(R+r1+r2)

That is not an equation. You had E=2 E r1 /(R+r1+r2). What does that give you for r1 in terms of R and r2?

 

[palkia]

I am getting R=r1-r2

 

[haruspex]

I am getting R=r1-r2

Right.