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Two unknown resistors. Need to find values of resistors.

  1. May 26, 2009 #1
    1. The problem statement, all variables and given/known data

    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.

    2. Relevant equations

    P = I^2 x R

    3. 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.
     
  2. jcsd
  3. May 26, 2009 #2

    jgens

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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.
     
  4. May 26, 2009 #3
    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
     
  5. May 26, 2009 #4

    jgens

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    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.
     
  6. May 26, 2009 #5
    just solve for r1 and substitute into the other....

    but are you sure those figures are correct? how did you get them?
     
  7. May 26, 2009 #6
    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? ?
     
  8. May 26, 2009 #7

    jgens

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    Unless I've misunderstood your question which is certainly possible, I believe the equation Req = R1R2/(R1 + R2) takes care of that consideration.
     
  9. May 26, 2009 #8
    Oh. Okay. I missed that. Thank you so much!
     
  10. May 26, 2009 #9

    jgens

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    No problem!
     
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