Conical Frustum Resistance (Friendlier Version)

Electricity and Magnetism Level 3

A solid resistor has the shape of a conical frustum, as shown below. At both ends of the frustum are perfectly conducting electrodes in the shape of circular disks. The resistivity of the material is uniform throughout.

What is the equivalent resistance between the two electrodes?


The answer is 0.47746.

Steven Chase by Steven Chase , 37, USA

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1 solution

The resistance of the truncated cone is 9 π \dfrac{9}{π} times the integral of d z ( 6 − z ) 2 \dfrac{dz}{(6-z)^2} within the limits 0 to 3, which yields 3 2 π \dfrac{3}{2π}

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