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Dissipation of Electric Power

  1. Dec 14, 2012 #1
    1. The problem statement, all variables and given/known data

    I want to ask about a question which is related to dissipation of electric power.
    Here's a quick picture of my problem:

    R1=R2=R3=R4
    R1 dissipates an electrical energy of 36 W
    Question: What is the electrical energy dissipated by R4?


    Please look at the circuit I've attached below.

    This is a Junior High physics questions which I don't understand. Thanks in advance.

    2. Relevant equations
    R=V2/P
    R=(Ωhm)
    P=(Watt)
    V=(Volt)


    3. The attempt at a solution
    I haven't made any attempt because it's confusing.
    Possible choices:
    a. 18 W
    b. 16 W
    c. 9 W
    d. 4 W
     

    Attached Files:

  2. jcsd
  3. Dec 14, 2012 #2

    lewando

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    Gold Member

    Another equation that might help is P=I2R. Is there anything in particular that you find confusing?
     
  4. Dec 14, 2012 #3

    CWatters

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    I suspect it appears confusing because not enough info is provided to calculate currents and voltages. Try thinking of it in terms of ratios.

    For example how does the current flowing in R4 compare to that in R2&3?
     
  5. Dec 14, 2012 #4

    lewando

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    To CW's point: if the notion of a "current divider" is in your toolbox, now would be a good time to bring it out :tongue2:.
     
  6. Dec 14, 2012 #5
    Well, not enough information is confusing, but I did it this way.

    First, I consider R1=R2=R3=R4=R

    Then, I calculate the resistance of the parallel circuit, that is, R2, R3, and R4.

    Rseries=R2+R3=2R

    1/Rparallel=(1/Rseries)+(1/R4)
    1/Rparallel=(1/2R)+(1/R)
    1/Rparallel=(1/2R)+(2/2R)
    1/Rparallel=3/2R
    Rparallel=2R/3

    P1=36 W
    Pparallel=2P1/3=24W
    Pseries : P4 = 1/2R : 1/R
    Pseries : P4 = 1/2 : 1
    Pseries : P4 = 1 : 2
    Pparallel=Pseries+P4=x + 2x=3x

    x=(24/3)W=8W
    P4=2x=2(8W)=16 W(answer is b)

    Is this correct?
     
  7. Dec 14, 2012 #6

    haruspex

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    Quite correct.
     
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