# Need to determine resistance of an object

• Kruum
In summary, the conversation discusses the calculation of resistance for a solid, truncated cone made of a material with resistivity p. The solution involves finding the linear function of r as a function of y and integrating to get the final resistance value, which is (p*h)/(pi*r1*r2). The question about the denominator being 4 was just a typing mistake.
Kruum

## Homework Statement

A material of resistivity p is formed into a solid, truncated cone of height
h and radii r_1 and r_2 at either end. Calculate the resistance of the cone
between the two flat ends.

You can find my awful sketch as a thumbnail.

## Homework Equations

R=pL/A ,where p is resistivity.

## The Attempt at a Solution

I know I need to calculate dR=(p*dy)/(pi*r^2). But I don't know what is r as a function of y.

#### Attachments

• E5.jpg
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Last edited:
Your attachment isn't approved yet, but isn't r a linear function of y or, more specifically, h-y? Try to construct a function that varies linearly from r1 to r2.

Where does the 4 come from in the denominator?

Mapes said:
Your attachment isn't approved yet, but isn't r a linear function of y or, more specifically, h-y? Try to construct a function that varies linearly from r1 to r2.

Where does the 4 come from in the denominator?

Thank you. I'll try your tip. And the 4 was just a typing mistake.

I uploaded the image. It can be found here: http://www.aijaa.com/v.php?i=3584252.jpg

Last edited:
This is what I came up with:

r = r2+y*(r1-r2)/h

If I integrate dR, it gives me (p*h)/(pi*r1*r2).

Does that look okay?

Last edited:
Looks good.

Thanks for the help, Mapes!

## 1. What is resistance and why do we need to determine it?

Resistance is the measure of an object's ability to resist the flow of electric current. It is an important factor in understanding and controlling electrical circuits and devices, and determining resistance allows us to calculate other important values such as voltage and current.

## 2. How is resistance measured?

Resistance is measured using a device called a multimeter, which passes a small amount of electric current through the object and measures the resulting voltage. The resistance can then be calculated using Ohm's Law (R=V/I), where R is resistance, V is voltage, and I is current.

## 3. What units is resistance typically measured in?

Resistance is typically measured in Ohms (Ω), named after the German physicist Georg Ohm who first described the relationship between voltage, current, and resistance in 1827.

## 4. How does the material and shape of an object affect its resistance?

The material and shape of an object can greatly affect its resistance. Materials with high electrical conductivity, such as metals, have lower resistance compared to materials with lower conductivity, like rubber or plastic. The shape of an object also plays a role, as longer and thinner objects tend to have higher resistance compared to shorter and thicker objects.

## 5. Can resistance change over time?

Yes, resistance can change over time due to various factors such as temperature, pressure, and physical damage. For example, as the temperature increases, the resistance of a conductor also increases. This is important to consider when designing and using electrical systems.

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