# Potential difference across a resistor

## 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

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]

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mfb
Mentor
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
Homework Helper
Gold Member
the total current in the circuit which came to be-E/(R+r1+r2)
No, you forgot something.

palkia
2E/R+r1+r2

haruspex
Homework Helper
Gold Member
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
Homework Helper
Gold Member
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
Homework Helper
Gold Member
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)

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

mfb
Mentor
So the potential difference across the interal resistor issame as terminal voltage of the battery?
Right.

palkia
haruspex
Homework Helper
Gold Member
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