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Resistive dissipation and Ohm's law

  1. Jun 8, 2017 #1
    1. The problem statement, all variables and given/known data
    A potential difference V is connected across a device with resistance R, causing current i through the device. Rank the following variations according to the change in the rate at which electrical energy is converted to thermal energy due to the resistance, greatest change first:
    (a) V is doubled with R unchanged,
    (b) i is doubled with R unchanged,
    (c) R is doubled with V unchanged,
    (d) R is doubled with i unchanged.

    2. Relevant equations
    $$P= {i^2} R$$
    $$P= \frac {V^2} R$$

    3. The attempt at a solution
    I know and understand that (a) and (b) result in ##P'=4P##, but I'm not sure if I judge (c) and (d) variations correctly. I guess that the answer to (c) and (d) is that there would be no change if the device obeys Ohm's law.
  2. jcsd
  3. Jun 8, 2017 #2


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    You can assume some values for V and R and check each condition. You have listed the correct equations.
    No change in what?
  4. Jun 8, 2017 #3
    No change in ##P##.
  5. Jun 8, 2017 #4


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    There will be changes in P according to the equations you've listed.
  6. Jun 8, 2017 #5
    I think I was wrong to worry about the Ohm's law, it is actually embedded in those two equations.
  7. Jun 8, 2017 #6


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    It looks like they only want you to worry about the changes that each choice asks about. Obviously if R is kept constant (in the first two), then a change in V results in a change in I, as well as a change in I would result in a change in V (per Ohm's Law). So the bottom two tell you that somehow the device has changed (maybe it is a potentiometer, which you can adjust), and they are able to configure the supply to remain constant in the listed variable.
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