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Homework Help: Finding an unknown resistance in an Electric Circuit

  1. Jul 25, 2010 #1
    1. The problem statement, all variables and given/known data
    When connected in series to a 110-V line, two resistors use one-fourth the power
    that is used when they are connected in parallel. If one resistor is
    2.0 kΩ, what is the resistance of the other?

    2. Relevant equations
    1/Rt = 1/R1 +1/R2 (total resistance in parallel)
    Rt = R1 + R2 (resistance in series)

    Power = Current x Voltage

    3. The attempt at a solution

    So far my attempts have fizzled, ending with negative numbers.

    Heres what I did:
    1) Set the two hypothetical circuits (series and parallel) equal to eachother by isolating the power:

    P1 = 110^2/0.25(R1+R2)
    P2 = 110^2(R1+R2)

    And then isolating for R2 and solving (since we have R1 = 2000 ohms)

    I ended up doing the quadratic equation and getting two negative numbers...

    Any help would be appreciated :)
  2. jcsd
  3. Jul 25, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Can you show why it this true?
    The term R1+R2 must be in the denominator.

    Anyway, I suggest that you work this symbolically. Find expressions

    Pseries = V2/Req,series
    Pparallel = V2/Req,parallel
    then take the ratio and say
    Pseries/Pparallel = 1/4.
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