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## Homework Statement

Hello! I have a problem where I need to develop and justify a hypothesis surrounding the relationship between the thickness (or diameter) of a nichrome wire and the temperature of water that it's submersed in over a time of 5 minutes. (proportionality statement and equations)

## Homework Equations

So far, I know that resistance is inversely proportional to cross-sectional area, and therefore:

R ∝ 1/A

R ∝ 1/∏r^2

R ∝ 1/∏(d/2)^2

and because 2 and ∏ are constant

R ∝ 1/d^2 (resistance is inversely proportional to diameter squared) (I think!)

Now, I've also researched Joule's law, which eventuates into:

Heat produced = Pt = VIt = V^2/Rt = I^2Rt

## The Attempt at a Solution

Now, I'm trying to get a relationship between diameter and ΔT, and I thought, so I have R ∝ 1/d^2, and P = V^2/R where V is a constant so P ∝ 1/R

and since P is the change in heat:

ΔT ∝ 1/R

OR

since thickness makes resistance go down

and less resistance makes ΔT (somehow)

then is R ∝ ΔT

and substituting so therefore:

ΔT ∝ 1/d

and I don't have much idea how to reason out what the graph will look like/why...

I think I've tied myself in knots... any help would be much appreciated! Thank you!:)

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