Two unknown resistors. Need to find values of resistors.

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Homework Help Overview

The problem involves determining the values of two unknown resistors connected in series and parallel with a battery, given specific power and current conditions for each configuration.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss using the power equation P = I^2 x R to derive equivalent resistances for both series and parallel configurations. There are attempts to form equations based on the given power and current values, with some participants expressing uncertainty about their calculations and the correctness of their derived equations.

Discussion Status

The discussion is ongoing, with participants sharing their equations and questioning the accuracy of their values. Some guidance has been offered regarding how to combine the equations for series and parallel resistances, but there is no explicit consensus on the final approach or solution.

Contextual Notes

Participants are working under the constraints of the problem statement and are attempting to reconcile their equations for series and parallel configurations. There is acknowledgment of potential mistakes in calculations and the need to clarify assumptions about the relationships between resistances.

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Homework Statement



When two unknown resistors are connected in series with a battery, the battery delivers 260 W and carries a total current of 5.00 A. For the same total current, 35.0 W is delivered when the resistors are connected in parallel. Determine the values of the two resistors.

Homework Equations



P = I^2 x R

The Attempt at a Solution



I tried to make two unknowns by plugging in numbers into the equations, but that's not working. I know that the voltage will be the same throughout the parallel circuit, and that the current will be the same throughout the series circuit, but I'm not quite sure where to go from there.
 
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Since P = I2R, we can solve for the equivalent resistance of the resistors.

Req = P/I2

When the resistors are in series, r1 + r2 = Req

Construct a similar equation for when the resistors are in parallel and you can solve for the values of the two resistors.
 
I have my two equations, but I'm having trouble putting the two equations together. I have r1 + r2 = 7 and 1/r1 + 1/r2 = 1/52
 
I'm not certain those values are correct, maybe I've made a mistake?

For series I get, Req = P/I2 = (260 W)/(5 A)2 = 10.4 ohms.

For parallel I get, Req = P/I2 = (35 W)/(5 A)2 = 1.4 ohms.

To get you started on solving the two equations, we know that R1 + R2 = 10.4 and R1R2/(R1 + R2) = 1.4. Combine these two equations.
 
just solve for r1 and substitute into the other...

but are you sure those figures are correct? how did you get them?
 
I think I must have forgotten to square "I"...your figures are correct. But then don't you also have to take into consideration that when you do 1/r1 + 1/r2 , that it equals 1/Req? ?
 
Unless I've misunderstood your question which is certainly possible, I believe the equation Req = R1R2/(R1 + R2) takes care of that consideration.
 
Oh. Okay. I missed that. Thank you so much!
 
No problem!
 

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