Potential difference across a resistor

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Homework Help Overview

The problem involves two cells with the same electromotive force (emf) but different internal resistances connected in series to an external resistance. The goal is to determine the value of the external resistance for which the potential difference across one of the cells is zero.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the total current in the circuit and the potential difference across the first cell. There are attempts to derive equations related to the circuit's behavior, with some questioning the assumptions made about voltage drops and the arrangement of terms in equations.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the equations and the implications of a zero potential difference across the first cell. Some guidance has been offered regarding the use of parentheses in equations, and there is an acknowledgment of the need to clarify the relationship between terminal voltage and internal resistance.

Contextual Notes

Participants are navigating through the implications of their calculations and the assumptions regarding the circuit setup, including the behavior of the internal resistances and the external resistance. There is a focus on ensuring clarity in mathematical expressions and the conditions under which the potential difference becomes zero.

palkia
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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]
 
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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)?
 
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Potential difference across r1is Er1/(R+r1+r2) so for zero potential difference r1=0 which looks weird
 
palkia said:
the total current in the circuit which came to be-E/(R+r1+r2)
No, you forgot something.
 
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2E/R+r1+r2
 
palkia said:
2E/R+r1+r2
Right, but please use parentheses correctly.
If the PD across the first battery is zero, what current would you expect?
 
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E=2E/(R+r1+r2) r1

But why are solving for the terminal voltage of the battery?
 
palkia said:
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.
 
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E-Ir1
 
  • #10
palkia said:
E-Ir1
I do not see how you got that from the equation in post #7. Please show your working.
 
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  • #11
haruspex said:
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
So the potential difference across the interal resistor issame as terminal voltage of the battery?
 
  • #13
palkia said:
So the potential difference across the interal resistor issame as terminal voltage of the battery?
Right.
 
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  • #14
palkia said:
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?
 
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  • #15
I am getting R=r1-r2
 
  • #16
palkia said:
I am getting R=r1-r2
Right.
 
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