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A torch cell is modelled as a thin inner cylindrical rod of radius 'a' inside a coaxial thin cylindrical shell of radius 'b', both of length l, with the gap filled by an electrolyte of resistivity rho so that current flows radially. If this cell drives an external resistor R, for what value of R is the Joule heating in R maximum?

1. R = (2*rho/(pi*l)) ln(b/a)
2. R = (rho/(pi*l)) ln(b/a)
3. R = (rho/(2*pi*l)) (b/a)
4. R = (rho/(2*pi*l)) ln(b/a)

Correct answer: R = (rho/(2*pi*l)) ln(b/a)

Solution

By the maximum power transfer theorem, R must equal the internal resistance, which for radial conduction between coaxial cylinders is (rho/(2*pi*l)) ln(b/a).

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