Model a torch battery of length $l$ to be made up of a thin cylindrical bar of radius â€˜aâ€™ and a concentric thin cylindrical shell of radius â€˜bâ€™ 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 :

Question

$R = {{2\rho } \over {\pi l}}\ln \left( {{b \over a}} \right)$

$R = {\rho \over {\pi l}}\ln \left( {{b \over a}} \right)$

$R = {\rho \over {2\pi l}}\ln \left( {{b \over a}} \right)$

$R = {\rho \over {2\pi l}}\left( {{b \over a}} \right)$

Solution

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