What is the Resistance of a Cylinder Conductor Made of Aluminum?

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In summary, the resistance of a cylindrical conductor made of aluminum with a radius of 2 mm and length of 2.33 m can be calculated using the formula R = ρL/A, where ρ is the resistivity and A is the cross-sectional area. The correct answer is 0.0051 Ω, which can be obtained by correcting the unit conversion of the radius from millimeters to meters.
  • #1
JSGandora
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Homework Statement


A cylindrical conductor of radius 2 mm and length 2.33 m is made of aluminum (p=2.75E-8[tex]\Omega[/tex]m). Calculate the Resistance of the conductor.


Homework Equations


Unknown (not given).


The Attempt at a Solution


I purely do not know how to do it. I'm thinking that we find the volume of the conductor then multiply it by the 2.75 but I don't think that works.
 
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  • #2
Look up "resistivity".
 
  • #3
Welcome to PF!

Hi JSGandora! Welcome to PF! :smile:

(have a rho: ρ and an omega: Ω :wink:)

Look at the units … Ω.m, not Ω.m3 :wink:

(actually, that m is really m2/m, ie area/length :biggrin:)
 
  • #4
Thank you! :)

I got the following equation:
[tex]R=\frac{\rho L}{A}[/tex]
where R is the resistance, p is the resistivity (by the way, what is the symbol for the "p"-like symbol called?), and A is the cross sectional area. Therefore, we have
[tex]R=\frac{2.75\Omega m\times10^{-8}(2.33m)}{(0.0002m)^2\pi}\approx0.51\Omega[/tex]?

The answer key says the answer is [tex]0.0051\Omega[/tex]. It looks like I am wrong by a factor of 100. I can't see why though...hmm...
 
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  • #5
erm :redface: … too many 0s in your 2mm ! :wink:

(and of course, it's called "rho")
 
  • #6
OHHH, failure on my part. Thanks for pointing that out, I thought there were 100 millimeters in one centimeter when I did that. ><
 

What is resistance?

Resistance is the measure of how difficult it is for electricity to flow through a material. It is measured in ohms (Ω) and is represented by the symbol R.

How do you calculate resistance?

The formula for calculating resistance is R = V/I, where R is the resistance in ohms, V is the voltage in volts, and I is the current in amps.

What factors affect resistance?

The factors that affect resistance include the material of the object, its length, its cross-sectional area, and its temperature. Materials with higher resistance, longer lengths, smaller cross-sectional areas, and higher temperatures will have higher resistance.

What is the difference between series and parallel circuits in terms of resistance?

In a series circuit, the total resistance is the sum of each individual resistance. In a parallel circuit, the total resistance is less than the smallest individual resistance. This is because in a parallel circuit, the current has multiple paths to flow through, reducing the overall resistance.

How does temperature affect resistance?

As temperature increases, the resistance of most materials also increases. This is because as the temperature rises, the atoms in the material vibrate more, making it harder for electrons to flow through. However, some materials, such as semiconductors, may have a decrease in resistance with an increase in temperature.

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