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Power and Resistance

  1. Mar 8, 2016 #1
    1. The problem statement, all variables and given/known data
    Rank the resistors according to to the rate at which energy is dissipated in them.

    Mazur1e.ch31.p88.jpg

    2. Relevant equations
    P = I2R
    P = V2/R
    Iin=Iout at a node

    3. The attempt at a solution
    First I looked considered the 20 Ω (top) and the 10 Ω(bottom). The current in them would be the same, so then applying the equations you get that the energy dissipated in the 20 Ω(top) > 10 Ω(bot).
    Next I looked at the 10, 5, and 20 Ω resistors in parallel. Resistors in parallel have the same voltage. Therefore, I concluded that the energy dissipated in the 5 Ω > 10 Ω > 20 Ω.
    Again I was thinking that the voltage would be same in the two 90 Ω resistors, so I have their energy dissipated equal, 90Ω(left) = 90Ω(right).

    I think I did that part right. However, I do not know how to go about comparing these three sets. I feel that it would be 5Ω > 10Ω > 20Ω > 90Ω = 90Ω > 20Ω(top) > 10Ω(bottom) since parallel circuits take more energy than a series configuration. Does this look correct? Thanks in advance for any help!
     
  2. jcsd
  3. Mar 8, 2016 #2
    find the equivalent of each parallel combination to reduce the circuit to a single mesh
    the resultant of (10,5,20) will be less than 5 so it will absorb the least amount of power
    (90,90)--> 45, the most amount.
    ______________________________
    "parallel circuits take more energy than series" you said, this is right when you are talking about the same resistors
    if connected (10,5,20) in series with a 5V voltage source they well absorb less power than if they are connected in parallel
     
  4. Mar 8, 2016 #3
    The equivalant resistance from the 10,5,20 is approximately 2.86 ohms, and for 90,90 is, as you said, 45 ohms. So you're saying that the order would then be [90=90]>20(top)>10(bottom)>[5>10>20]?
     
  5. Mar 8, 2016 #4
  6. Mar 8, 2016 #5

    SammyS

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    That is the correct order. The analysis you have looks a bit shy of actually showing that order, unless I missed something.

    For instance, if there was a 30 Ω resistor replacing the 20 Ω resistor the order would be different.

    The pair of 90 Ω resistors in parallel would dissipate more power than a 30 Ω resistor which is in series with the pair. However, combined they would dissipate less than twice the power, so that each dissipates lees than the 30 Ω resistor.
     
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