Resistance of a fructum-shaped bar

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In summary, the conversation discusses the calculation of resistance for a bar shaped like a frustum. The formula for resistance is given, but the problem is incorporating the formula for volume into it. The possibility of treating the frustum as a cube with the same volume is suggested as a solution. The conversation also clarifies that the correct spelling is frustum, which is similar to a cone but with the sharp end cut off.
  • #1
Icheb
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I have to calculate the resistance of a bar that is shaped like a fructum and I'm only given the radius of both ends, not its length.

The formula to calculate the resistance in general is

[tex]R = \rho * \frac{l}{A}[/tex]

And the formula for the volume of a fructum is

[tex]V = \frac{\pi * l}{3} (r^2_2 * r_2r_1 * r^2_1)[/tex]

My problem is that I have difficulties incorporating the formula for the volume into the formula for the resistance.

Would it be possible to calculate the volume of the fructum (which would be dependant on l) and treat it like it's a cube with the same volume? That way, I could use [tex]A = \frac{V}{l}[/tex], then divide the volume by l and enter it into the formula for R.

Other than that, I have no idea what approach to take.
 
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  • #2
Sorry, looked as best I can.

No idea what a fructum is.
 
  • #3
Sorry, I misspelled it. I meant a frustum. It's like a cone, but with the "sharp" end cut off.
 

FAQ: Resistance of a fructum-shaped bar

What is the resistance of a fructum-shaped bar?

The resistance of a fructum-shaped bar is a measure of how difficult it is for electricity to flow through the bar. It is typically measured in ohms (Ω).

How is the resistance of a fructum-shaped bar calculated?

The resistance of a fructum-shaped bar is calculated using Ohm's Law, which states that resistance is equal to voltage divided by current. It can also be calculated using the formula R = ρL/A, where ρ is the resistivity of the material, L is the length of the bar, and A is the cross-sectional area.

What factors affect the resistance of a fructum-shaped bar?

The resistance of a fructum-shaped bar is affected by several factors, including the material of the bar, its length and cross-sectional area, and the temperature of the bar. It also depends on the type of current flowing through the bar and the presence of any impurities or defects in the material.

How does the shape of the bar affect its resistance?

The shape of the bar can affect its resistance by altering its length and cross-sectional area. A longer bar will have higher resistance, while a larger cross-sectional area will have lower resistance. The shape can also impact the flow of current, which can affect resistance.

What is the practical application of understanding the resistance of a fructum-shaped bar?

Understanding the resistance of a fructum-shaped bar is important for designing and building electrical circuits and systems. It also has practical applications in fields such as electronics, engineering, and physics. Knowing the resistance of a material can also help in troubleshooting issues with electrical components and identifying potential hazards.

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