Model a torch battery of length l to be made up of a thin cylindrical bar of radius a and a concentric thin cylindrical shell of radius b filled in between with an electrolyte of resistivity ρ (see figure). If the battery is connected to a resistance of value R , the maximum Joule heating in R will take place for :

Question

Model a torch battery of length l to be made up of a thin cylindrical bar of radius a and a concentric thin cylindrical shell of radius b filled in between with an electrolyte of resistivity ρ (see figure). If the battery is connected to a resistance of value R , the maximum Joule heating in R will take place for :, R = ρ 2 π ℓ b a, R = ρ 2 π ℓ ln b a, R = ρ π ℓ I n b a, R = 2 ρ π ℓ ln b a

MARKS App · Accepted Answer

Let a small elementary cylinder in the shell of thickness d r . The resistance of a wire is given by R = ρ L A . Here ρ is the resistivity of the material. The resistance of small element d R = ρdr 2 πr l Integrating both sides, ⇒ R = ρ 2 πl ∫ a b dr r ⇒ R = ρ 2 πl l n b a

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