Estimating resistance of a wire

[jegues]

Homework Statement

See figure.

Homework Equations

N/A.

The Attempt at a Solution

I'm not to sure how I'm suppose to estimate the resistance of the wire based on its length and diameter.

I'll take an educated guess and try to cancel units to get what I want.

If,

\rho = 5.5 * 10^{-8} \Omega m

Then I want to cancel the meters out and I'll be left with ohms which would be my estimated resistance for this filament.

But which measurement would I use to cancel my meters out? The length of the wire? (2cm in this case) Or the diameter of the wire? (25\mum)

I thought of calculating the surface area of the circle at the tip of the wire, and summing up an infinite amount of circles across the length of the wire and then trying to solve for the resistance, but I keep getting some pretty weird numbers.

Oh, and when it says compare your answer with the value obtained in part b, I obtained a reistance of 360 ohms.

Does anyone have any ideas on how to solve this?

 

[Zryn]

As the cross sectional area of a piece of wire increases (like water down a bigger pipe) there is less resistance. Therefore the resistance of the wire is inversely proportional to cross sectional area.

As the length of a piece of wire increases, there is more resistance (more force to get the water to the other end). Therefore the resistance of the wire is proportional to the length.

The last factor is a characteristic of the wire, known as the resistivity and designated the Greek symbol rho, which you are given.

Therefore, R = \frac{L*\rho}{A}

Note that this gives R = \frac{m*\Omega m}{m^{2}} = \Omega

I would agree with your 360Ohms initial answer too.

 

[jegues]

Thank you, this cleared up all the confusion I had!