What is the resistance of a hollow aluminum cylinder with given dimensions?

In summary, the question asks for the reading on an ohmmeter connected between the inner and outer surfaces of a hollow aluminum cylinder with dimensions of 2.5 m in length, 3.20 cm inner radius, and 4.60 cm outer radius. The formula for resistance is R = (resistivity of hollow cylinder * length of hollow cylinder) / area, and the voltage is equal to the current multiplied by resistance. The problem lies in determining which area to use in the calculation, as the inner and outer areas are different. After considering the effects of length and cross-sectional area on resistance, the correct area to use is the cross-sectional area of the current flow.
  • #1
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Homework Statement



A hollow aluminum cylinder is 2.5 m 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=[(resistivity of hollow cylinder)*(length of hollow cylinder)]/Area

V=IR

The Attempt at a Solution



I was given the resisitivity of the aluminum cylinder and the length, but I am at a loss: the area inner part of the cylinder is less than the area of the outer part of the cylinder. My question is this: I don't know what area to use: do I use the area of the outer cylinder or the inner cylinder. Thanks.
 
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  • #2
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A is the cross-sectional area of the current flow.
Think about why both the length and A are in the equation for resistance. Imagine their effects on a microscopic level.

Can you do it now?
 

1. What is a hollow aluminum cylinder?

A hollow aluminum cylinder is a cylindrical tube made of aluminum that has an empty space or cavity inside it.

2. What are the properties of a hollow aluminum cylinder?

Hollow aluminum cylinders have a high strength-to-weight ratio, are corrosion-resistant, and have good thermal and electrical conductivity.

3. What are the common uses of a hollow aluminum cylinder?

Hollow aluminum cylinders are commonly used in construction, transportation, and manufacturing industries for applications such as structural support, fuel tanks, and heat exchangers.

4. How is a hollow aluminum cylinder made?

Hollow aluminum cylinders are typically made through an extrusion process, where a heated aluminum billet is forced through a die to create the desired shape. The extruded cylinder is then cut to the desired length and cooled.

5. How can the strength of a hollow aluminum cylinder be increased?

The strength of a hollow aluminum cylinder can be increased by heat treating, which involves heating the cylinder to a high temperature and then cooling it rapidly. This process can also improve the corrosion resistance and hardness of the cylinder.

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