Wires with constant power and increasing voltage

[MathewsMD]

My question is in the attached image.
Before going right at it, I thought it would be best to clarify a few details.

Ohm's Law only shows that current and potential are linearly related, correct? So R is constant in the case of a material that follows Ohm's Law (metal conductors for the most part, right?). But regardless of the material, isn't resistivity and as a result resistance of an object w/ constant length and surface also a constant? Or does it vary with current/potential? Isn't V = IR the definition of resistance? Do all three variables change in no particular pattern for materials that do not follow Ohm's Law?

Also, does heating in a wire depend on BOTH resistance and current? Are there any other factors?

Now, to the attached question, I am assuming that the wire follows Ohm's Law (is that a reasonable assumption?). I've circled the correct answer, but cannot quite understand why C and E are wrong. We know P is constant, and so is R if it follows Ohm's Law (once again, would R be constant if the material did not obey Ohm's Law?). Thus b is false since resistance of the wires stays the same. And even if it did change, P = V²/R, so resistance would not decrease. Also, isn't insulation related to resistance? Assuming constant resistance, this property does not change, so d is wrong.

Now, I know P = IV, and if V increases then I decreases. But if V= IR and R is a constant, if V increases doesn't I increases as well? What am I missing here? Also, isn't the IR drop simple V (V=IR). If V increases, then doesn't IR as well?

Just so you know, we were told all answers but a are false. Any comments on why and could you possibly critique my reasoning as well? Thanks!

 

[NascentOxygen]

Have you worked out what the current would be in the two different cases?

Yes, assume resistance does not change significantly with current or voltage, in cables.

 

[MathewsMD]

Have you worked out what the current would be in the two different cases?

Yes, assume resistance does not change significantly with current or voltage, in cables.

We didn't really calculate much with this question in class, we just went over the choices with reasoning.

I understand that since P = constant = IV, that current would decrease in this case. I am assuming increased current (or resistance for other cases) increases heat production, which is why a would be right. By problem lies with why V = IR is not exactly telling us the same thing. I know current decreases with increasing voltage when power is constant as given by P = IV, but then is V/I = R and R is also a constant, how would increasing V decrease I? Also, isn't IR the same thing as potential, so as potential, V, increases s does the IR drop?

 

[NascentOxygen]

You are getting your V's confused. There is the V related to supply voltage, and there is the V related to losses in cable resistance.

 

[MathewsMD]

You are getting your V's confused. There is the V related to supply voltage, and there is the V related to losses in cable resistance.

Hmmm...okay...do you mind expanding on this a bit or referring me to any sources you think are relevant? I kind of thought they were both the related...

Also, any answers for the other questions I posted?