Potential difference across a resistor

  • #1
52
2

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]
 

Answers and Replies

  • #2
34,962
11,147
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)?
 
  • Like
Likes palkia
  • #3
52
2
Potential difference across r1is Er1/(R+r1+r2) so for zero potential difference r1=0 which looks weird
 
  • #4
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
34,840
6,113
the total current in the circuit which came to be-E/(R+r1+r2)
No, you forgot something.
 
  • Like
Likes palkia
  • #5
52
2
2E/R+r1+r2
 
  • #6
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
34,840
6,113
2E/R+r1+r2
Right, but please use parentheses correctly.
If the PD across the first battery is zero, what current would you expect?
 
  • Like
Likes palkia
  • #7
52
2
E=2E/(R+r1+r2) r1

But why are solving for the terminal voltage of the battery?
 
  • #8
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
34,840
6,113
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.
 
  • Like
Likes palkia
  • #9
52
2
E-Ir1
 
  • #10
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
34,840
6,113
E-Ir1
I do not see how you got that from the equation in post #7. Please show your working.
 
  • Like
Likes palkia
  • #11
52
2
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)
 
  • #12
52
2
So the potential difference across the interal resistor issame as terminal voltage of the battery?
 
  • #13
34,962
11,147
So the potential difference across the interal resistor issame as terminal voltage of the battery?
Right.
 
  • Like
Likes palkia
  • #14
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
34,840
6,113
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?
 
  • Like
Likes palkia
  • #15
52
2
I am getting R=r1-r2
 
  • #16
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
34,840
6,113
  • Like
Likes palkia

Related Threads on Potential difference across a resistor

Replies
2
Views
22K
Replies
1
Views
8K
Replies
3
Views
817
Replies
3
Views
3K
  • Last Post
Replies
2
Views
15K
Replies
2
Views
8K
Replies
2
Views
933
Replies
1
Views
652
Replies
24
Views
2K
Top