How Does Power Depend on Resistance in Electrical Circuits?

[khiamabbasi]

my question isthatthe relation(p=I2R)where 2 means sqare shows power is directly propotional to resistane but the relationp[p=v2/R]shows that power is inversely propotioonal to R which is corect i think in many ways but could not find siolution

 

[Manchot]

EDIT: I made the post that was here when it was in a completely different topic, so it's now irrelevant.

 

[Fermat]

Since V = IR, the two expressions are equivalent.

You get the 2nd expression simply by substituting I = V/R in the 1st expression.

 

[khiamabbasi]

i need this answer theroraticaly not mathimatically if u mind it i m soory

 

[Diane_]

The problem is that in the expression I^2R, both the I and the R depend on the resistance. Whether power is directly or inversely proportional to resistance depends on what you're holding constant. If you hold the current constant, then the power will vary directly as the resistance - double the resistance, you double the power. Note, though, that you'd have to vary the voltage significantly to hold the current constant while changing the resistance.

On the other hand, if you hold the voltage constant, then power varies inversely as the resistance - double the resistance, you halve the power. Notice again, though, that the current will change significantly as you vary the resistance if you hold the voltage constant.

The point is that the actual relation (more or less) for power is P = IV. The other formulas you cite come from applying Ohm's Law to this one. Since I and V both depend on the resistance of the circuit, there's no simple answer to "how does power depend on resistance".

Is that sufficient?