JEE Main20203 Sep 2020Morning ShiftPhysicsCurrent ElectricityActual
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 :
Options
- AR = ρ 2 π ℓ b a
- BR = ρ 2 π ℓ ln b a
- CR = ρ π ℓ I n b a
- DR = 2 ρ π ℓ ln b a
Correct answer
B. R = ρ 2 π ℓ ln b a
Step-by-step solution
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