A material of resistivity p_gur=0.255 Ohm is formed into the shape of a truncate

Question

A material of resistivity p_gur=0.255 Ohm is formed into the shape of a truncated cone of altitude h=0.0557 m as shown in the figure. The bottom end has radius b=0.0760 m, and the top end has radius a=0.0368 m. Assume that the current is distributed uniformly over any circular cross section of the cone, so that the current density does not depend on radial position. (The current density does vary with position along the axis of the cone.) Find the resistance between the two ends, use "ohm" for the units.

Explanation / Answer

resistivity of given material, rho=0.255 ohm*m

cone altitude, h=0.0557 m

bottom end radius, b=0.076 m

top end radius, a=0.0368 m

use,

resistance of truncated cone shape is,

R=rho*h/(a*b)

R=0.255*0.0557/(0.076*0.0368)

R=5.08 ohms

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