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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 ' $b$ ' fille 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
  • A$R =\frac{2 \rho}{\pi l} l n \left(\frac{ b }{ a }\right)$
  • B$R =\frac{\rho}{\pi l} \ln \left(\frac{ b }{ a }\right)$
  • C$R =\frac{\rho}{2 \pi l}\left(\frac{ b }{ a }\right)$
  • D$R =\frac{\rho}{2 \pi l} \ln \left(\frac{ b }{ a }\right)$
JEE MAIN 2020, Diffcult
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