How to find a hollow cuboid's resistance

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In summary, the resistance between two points on the same face but not lying on the edges of a hollow cuboid can be found by using numerical methods to solve differential equations, as the distribution of electric field and current is not uniform and they depend on each other. However, if the cuboid is crumbled, meaning broken into pieces, the resistance between those same points will change. But if the cuboid is crumpled, meaning deformed without breaking off any pieces, the resistance will not change as long as the surfaces don't touch each other and the material is not stretched. To determine the resistance in a practical manner, an experiment can be conducted using household materials and a digital multimeter with an ohm-meter mode.
  • #1
hackhard
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how to find a hollow cuboid's resistance between two points on same face but not lying on the edges. the line joining 2 points is parallel to the length of the cuboid.
resistivity is uniform
another related doubt - will resistance between those same points change if the cuboid is deformed (the box is crumbled)
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  • #2
If you are looking for a simple formula I am afraid you won't find it. The distribution of electric field and current is not uniform. And they depend on each other.
You probably need numerical methods to solve the differential equations.
Maybe some empirical formula may be found, if such is used in some industrial application.
 
  • #3
hackhard said:
will resistance between those same points change if the cuboid is deformed (the box is crumbled)
 
  • #4
hackhard said:
will resistance between those same points change if the cuboid is deformed (the box is crumbled)
"Crumbled" means broken into pieces, as when a cookie is broken into crumbs. Answer: Yes
"Crumpled" means deformed or its shape changed without breaking off any pieces. Answer: No. If surfaces don't touch each other and the material is not stretched.
 
  • #5
I'm not so sure about this. As the theoretical treatment is very complicated, I suggest to simply to an experiment, measuring the resistance. I guess it's not so difficult to do qualitatively with house-hold means. Just use aluminum foil and wrap a cubic box (easily tinkered with some cardboard. Also nearly any modern digital multimeter has an ohm-meter mode :-).
 

FAQ: How to find a hollow cuboid's resistance

How do I calculate the resistance of a hollow cuboid?

To calculate the resistance of a hollow cuboid, you will need to know its dimensions (length, width, and height) and the material's resistivity. The formula for resistance is R = (p * L) / A, where R is resistance, p is resistivity, L is length, and A is cross-sectional area. For a hollow cuboid, the cross-sectional area is the difference between the outer and inner cross-sectional areas.

What is the unit of measurement for resistance?

The unit of measurement for resistance is ohms (Ω). This unit is named after the German physicist Georg Ohm, who first described the relationship between voltage, current, and resistance in an electric circuit.

Can I use the same formula to find the resistance of a solid cuboid?

Yes, the same formula can be used to find the resistance of a solid cuboid. The only difference is that for a solid cuboid, the cross-sectional area is the same as the outer cross-sectional area, since there is no inner area. This means that the formula becomes R = (p * L) / (L * W), where L is length and W is width.

How does the resistivity of a material affect the resistance of a hollow cuboid?

The resistivity of a material is a measure of how well it conducts electricity. Materials with higher resistivity will have a higher resistance, while materials with lower resistivity will have a lower resistance. This means that the type of material used to make the hollow cuboid will impact its resistance.

Are there any other factors that can affect the resistance of a hollow cuboid?

Yes, there are other factors that can affect the resistance of a hollow cuboid. These include the temperature of the material, the shape and size of the hollow cuboid, and the presence of any impurities in the material. Additionally, the length and width of the hollow cuboid can also impact its resistance.

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