Finding pd given r, R, and emf?

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Homework Help Overview

The discussion revolves around calculating the potential difference across a 23 ohm load resistor connected to a battery with a specified emf and internal resistance. The problem involves concepts from electrical circuits, particularly Ohm's law and the impact of internal resistance on voltage measurements.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between emf, internal resistance, and the load resistor. There are attempts to derive current using different formulations, and questions arise regarding the correct application of total versus external resistance in calculations.

Discussion Status

Some participants have provided guidance on the correct interpretation of the equations involved, while others express confusion about the use of total resistance versus just the external resistance. There is acknowledgment of mistakes in previous calculations, and a participant indicates they have reached an understanding after considering feedback.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. There is an emphasis on ensuring clarity in the definitions of variables used in the equations.

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Homework Statement


What potential difference is measured across
a 23 ohm load resistor when it is connected
across a battery of emf 7.99 V and internal
resistance 0.555 ohms
Answer in units of V


Homework Equations


V=IR
V=emf - Ir


The Attempt at a Solution


V=IR
emf-Ir=IR
(emf/I)-r=R
emf/I=R-r
I=(emf/(R-r))
I=(7.99/((23+.555)-.555)))
I=0.34739

V=IR
V=(0.34739)(23.555)
V=8.182802174
INCORRECT
 
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ugodzilla said:

Homework Statement


What potential difference is measured across
a 23 ohm load resistor when it is connected
across a battery of emf 7.99 V and internal
resistance 0.555 ohms
Answer in units of V

Homework Equations


V=IR
V=emf - Ir

The Attempt at a Solution


V=IR
emf-Ir=IR
(emf/I)-r=R
emf/I=R-r
That should be R+r in that last equation, since you are adding +r to both sides of the equation before it.
I=(emf/(R-r))
I=(7.99/((23+.555)-.555)))
R is simply 23 ohms, not 23+.555
I=0.34739

V=IR
V=(0.34739)(23.555)
V=8.182802174
INCORRECT
 
so,
I=7.99/22.445
I=0.355598
then,
V=(0.355598)(23) ?
or V=(0.355598)(23.555)

I don't understand why I'm not supposed to use the total resistance as opposed to just the external resistance.
 
I tried out both ways, and each answer was deemed incorrect.
8.385139229
and
8.187569615
 
I finally got! I didn't see the comment you made about the mistake in my simplifying! Thanks for the help
 
ugodzilla said:
so,
I=7.99/22.445
I don't understand why I'm not supposed to use the total resistance as opposed to just the external resistance.
When you said that "V=emf - Ir", that V is the voltage across the 23 ohm resistor.

And you also said "V=IR" -- the same V here. Since V is the voltage across the 23 ohm resistor, R must be referring to that resistor.

ugodzilla said:
I finally got! I didn't see the comment you made about the mistake in my simplifying! Thanks for the help
You're welcome, glad it worked out. :smile:
 

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