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Question

A material of resistivity ρ is formed in the shape of a truncated cone of altitude h. The top end has a radius "a" while bottom end has a radius "b". Assuming a uniform current density through any circular cross-section of the cone, find the resistance between the two ends.



A

ρh2πab

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B

2ρhπab

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C

ρhπab

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D

ρhπ(a+b)

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Solution

The correct option is C

ρhπab



Here, ray=bahy=h(ra)bady=h(ba)dr
Resistance of the thin elementary disc is dR=ρdyπr2=ρπh(ba)drr2
Rtotal=ρhπ(ba)ba1r2dr=ρhπ(ba)[1r]ba=ρhπ(ab)


Physics

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