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Relation of resistance to power dissipation

  1. Apr 7, 2012 #1
    Equation (p=i^2 * R) seems to suggest that the rate of increase of thermal energy in a resistor is reduced if the resistance is made less.

    "Eq" : p =v^2/R seems to suggest just the apposite .

    How do you reconcile this apparent paradox?
     
  2. jcsd
  3. Apr 7, 2012 #2

    cepheid

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    Re: Important Question

    You reconcile it by noticing that, if V is constant, then you cannot reduce R without increasing I (ohm's law). If you reduce R by a factor of 2, then you increase I by a factor of 2, which means that, using the first equation, your power changes by a factor of (2^2)/2 = 4/2 = 2.

    Using the second equation, your power changes by a factor of 1/(1/2) = 2.
     
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