Relation of resistance to power dissipation

[omari_yousef]

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?

 

[cepheid]

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?

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.