Resistance of a hollow aluminum cylinder

In summary, the question asks for the resistance between the inner and outer surfaces of a hollow aluminum cylinder, with given dimensions and assuming all surfaces are equipotential. Using the equation R=(\rho/2piL)*ln(R/r), the resistance can be calculated, but the exact method of connection between the two surfaces is not specified and may affect the result.
  • #1
digitaleyes
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Homework Statement



A hollow aluminum cylinder is 2.50m long and has an inner radius of 3.20 cm and an outer radius of 4.60 cm. Treat each surface (inner, outer, and the two end faces) as an equipotential surface.

At room temperature, what will an ohmmeter read if it is connected between the inner and outer surfaces?

Homework Equations



R=4.60cm
r=3.20cm

R=[tex]\rho[/tex]L/A

and possibly

R=([tex]\rho[/tex]/2piL)*ln(R/r)

The Attempt at a Solution



Well, the first part of the question (not asked here) was to find the resistance from one end of the hollow cylinder to the other (the faces). I found that: 2.00*10-5 [tex]\Omega[/tex]s. The problem does not say that the current is flowing radially through the cylinder though, but is that to be assumed for doing this second part? Or not? I plugged everything into the second equation, but the answer is wrong. Should the resistance be the same as it is from end to end? Is it 0?
*confused*
 
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  • #2
It is a curious question. Connected exactly how to the two surfaces? Connection at infinitely small points will lead to infinite resistance, so it seems we must assume the contact is spread, equipotentially, across each entire cylindrical surface.

That should mean your second equation is appropriate. See e.g. https://www.miniphysics.com/uy1-resistance-of-a-cylindrical-resistor.html.
Can't say any more without seeing your working and/or answer.
 

What is the resistance of a hollow aluminum cylinder?

The resistance of a hollow aluminum cylinder depends on several factors such as the dimensions of the cylinder, the material properties of aluminum, and the temperature. It can be calculated using the formula R = (ρ * L) / A, where ρ is the resistivity of aluminum, L is the length of the cylinder, and A is the cross-sectional area.

How does the length of the cylinder affect its resistance?

The longer the cylinder, the higher the resistance. This is because the longer the path for the current to flow through, the more collisions the electrons will have with the material, resulting in a higher resistance.

What is the effect of temperature on the resistance of a hollow aluminum cylinder?

The resistance of a hollow aluminum cylinder increases as the temperature increases. This is due to the fact that as the temperature rises, the atoms in the material vibrate more and create more obstacles for the electrons to flow through, thus increasing the resistance.

How does the cross-sectional area affect the resistance of a hollow aluminum cylinder?

The larger the cross-sectional area, the lower the resistance. This is because a larger area allows for more space for the electrons to flow through, resulting in fewer collisions and a lower resistance.

What other factors can affect the resistance of a hollow aluminum cylinder?

Aside from the dimensions and temperature, the purity of the aluminum and the presence of impurities can also affect the resistance. A higher purity aluminum will have a lower resistance, while the presence of impurities can increase the resistance.

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