What's the Resistance in a Circular Pan with a Metal Disk?

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SUMMARY

The resistance measured from the side of a metal disk placed at the center of a circular pan filled with a resistive solution is calculated using the formula R = (p * ln(b/a)) / (2πL). Here, 'p' represents the resistivity of the solution, 'b' is the radius of the pan, 'a' is the radius of the disk, and 'L' is the height of the disk. The solution involves integrating the resistance of thin rings between the radii 'a' and 'b' to derive the total resistance.

PREREQUISITES
  • Understanding of electrical resistance and the formula R = pL/A
  • Familiarity with logarithmic functions and their applications in physics
  • Basic knowledge of cylindrical coordinates and integration techniques
  • Concept of resistivity in conductive materials
NEXT STEPS
  • Study the derivation of resistance in cylindrical geometries
  • Learn about the integration of functions in polar coordinates
  • Explore the properties of logarithmic functions in physical applications
  • Investigate the concept of resistivity in various materials and its impact on electrical circuits
USEFUL FOR

Physics students, electrical engineering students, and anyone studying the principles of resistance in conductive materials.

kjintonic
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Homework Statement



A circular pan of radius b has a plastic bottom and metallic side wall of height h. It is filled with a solution of resistivity p. A metal disk of radius a and height h is placed at the center of the pan. The side and disk are perfect conductors. what's the resistance measured from the side of the disc. the answer is suppose to be (p*ln(b/a))/(2'pie'L)

Homework Equations



R= pL/A

The Attempt at a Solution


I kinda don't know how to start. the solution makes me confused
 
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What would be the resistance of a thin ring, with height h, radius r, and thickness Δr?

Once you get that, think of how to combine many such rings to fill the space between r=a and r=b.
 

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