Relation of resistance to power dissipation

  • #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?
 

Answers and Replies

  • #2
cepheid
Staff Emeritus
Science Advisor
Gold Member
5,192
36


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.
 

Related Threads on Relation of resistance to power dissipation

  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
4
Views
4K
Replies
6
Views
16K
Replies
29
Views
5K
  • Last Post
Replies
3
Views
2K
Replies
4
Views
9K
  • Last Post
Replies
9
Views
2K
  • Last Post
Replies
2
Views
25K
Replies
1
Views
5K
  • Last Post
Replies
10
Views
21K
Top