How Do You Calculate Resistance in a Radial Cylinder System?

• asi123
R1 and R2 are inner and outer radii respectively, L is the length of the cylinder and ρ is the resistivity of the material used.In summary, the conversation is about finding the resistance of a cylindrical system with given radius and length, for a current going from the inner cylinder to the outer cylinder. The solution provided involves using the resistance formula, taking into account the radii, length, and resistivity of the material. The correctness of the solution is uncertain and the person is seeking clarification.
asi123

Homework Statement

Hey guys.
So I got this cylinder with radius R1, R2 and length L as you can see in the pic.
I need to find the resistance of the system for a current that goes from the inner cylinder to the outer cylinder (radial style ).

I uploaded my solution but I'm not so sure about it, can you please tell me if what I did is right?

The Attempt at a Solution

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Hi, Not sure if you sorted this or not, but the correct solution I believe is:-

Resistance (ohms) = (Ln(R2)-Ln(R1)).ρ/(Pi.L)

I would like to commend you for taking on this problem and attempting to find a solution. From your diagram, it seems like you have correctly identified the two cylinders with radii R1 and R2 and length L. To find the resistance of the system, we can use the formula R = ρL/A, where ρ is the resistivity of the material, L is the length of the conductor, and A is the cross-sectional area of the conductor.

In this case, the current is flowing radially from the inner cylinder to the outer cylinder. Since the current is flowing in a circular path, we can use the circumference C = 2πr as the length of the conductor. The cross-sectional area A can be calculated as the difference between the areas of the two cylinders, A = π(R2^2 - R1^2).

Therefore, the resistance of the system can be calculated as R = ρ(2πr)/(π(R2^2 - R1^2)) = 2ρr/(R2^2 - R1^2).

However, it is important to note that this formula assumes that the resistivity of the material is constant along the length of the cylinders. If the resistivity varies, then the resistance will also vary along the length of the conductor.

I would also recommend double-checking your calculations and units to ensure that your final answer is in the correct units and makes sense in the context of the problem. I hope this helps and good luck with your further studies!

1. What is resistance through a cylinder?

Resistance through a cylinder refers to the opposition or hindrance that a material or medium presents to the flow of electric current through it. This resistance is measured in ohms and is dependent on factors such as the material, length, and diameter of the cylinder.

2. How is resistance through a cylinder calculated?

The resistance through a cylinder can be calculated using Ohm's Law, which states that resistance is equal to the voltage across the cylinder divided by the current passing through it. Alternatively, 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 cylinder, and A is the cross-sectional area.

3. How does the material of the cylinder affect resistance?

The material of the cylinder plays a significant role in determining its resistance. Materials with high resistivity, such as rubber, have a higher resistance compared to materials with low resistivity, such as copper. This is because the electrons in high resistivity materials experience more collisions, hindering their flow and resulting in higher resistance.

4. How does the length of the cylinder affect resistance?

The length of the cylinder also has an impact on its resistance. The longer the cylinder, the greater the distance the electrons have to travel, leading to more collisions and a higher resistance. This relationship is inversely proportional, meaning that as the length increases, the resistance also increases.

5. Can the resistance through a cylinder be changed?

Yes, the resistance through a cylinder can be changed by altering its length, diameter, or material. Additionally, by adjusting the voltage or current passing through the cylinder, the resistance can also be changed. This property of resistance allows for the control and regulation of electric current, making it an essential concept in fields such as electrical engineering and physics.

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