Resistance of copper vs glass problem

[cseet]

Hi all,
I've this question and I don't know how to go about... can somebody pls assist?
thanks
question:
a cylinder of glass 1cm long has a resistivity of 10E12 ohm meter. how long would a copper wire of the same cross sectional areqa need to be to have the same resistance as the glass cylinder?

thanks in advance.
cseet

 

[Chi Meson]

Resistance is directly proportional to both length and resistance. If cross-sectional area is constant, then to retain the same total resistance, the length of the copper wire will be the same fraction less as its resistivity is to that of glass. resistivityglass /resistivitycopper = lengthcopper / lengthglass

 

[M98Ranger]

Hi cseet,

This is a great question! To find the length of the copper wire that would have the same resistance as the glass cylinder, we can use the formula for resistance, R = ρ * (L/A), where ρ is the resistivity, L is the length, and A is the cross-sectional area.

First, let's find the resistivity of copper. According to the Engineering Toolbox, the resistivity of copper is approximately 1.68E-8 ohm meter. Now, we can plug in the values for resistivity and cross-sectional area (which we can assume to be the same for both the glass cylinder and the copper wire since they have the same cross-sectional area) into the formula:

10E12 = (1.68E-8) * (L/A)

Solving for L, we get L = 5.952E19 meters. That's a very long length! To put it into perspective, that's approximately 63 billion times the distance from the Earth to the Sun. So, in short, the copper wire would need to be extremely long to have the same resistance as the glass cylinder.

I hope this helps! Let me know if you have any other questions or if you need further explanation.