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: (a) R = (2ρ)/(π l)ln (b/a) (b) R = (ρ)/(π l)ln (b/a) (c) R = (ρ)/(2π l)ln (b/a) (d) R = (ρ)/(2π l)(b/a)

Answer: (c). Internal resistance: current flows radially through shells of area 2π r l, so rint = ∫ab (ρ dr)/(2π r l) = (ρ)/(2π l)/a. Power in R is maximum when R = rint (maximum power transfer). R = (ρ)/(2π l)/a. The answer is (c).

Model a torch battery of length l to be made up of a thin cylindrical… | JEE Main 2020 (3 Sep, Shift 1)

Q42JEE Main 2020 · 3 SEP · SHIFT 1Difficult

Ohm's Law, Resistivity & Temperature

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 $\rho$ (see figure). If the battery is connected to a resistance of value R, the maximum Joule heating in R will take place for:

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Answer: (c)

Internal resistance: current flows radially through shells of area $2\pi r l$ , so $r_{int} = \int_a^b \dfrac{\rho\,dr}{2\pi r l} = \dfrac{\rho}{2\pi l}\ln\dfrac{b}{a}$ .
Power in $R$ is maximum when $R = r_{int}$ (maximum power transfer).
$R = \dfrac{\rho}{2\pi l}\ln\dfrac{b}{a}$ . The answer is (c).

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