Model a torch battery of length L to be a made up of a thin cylindrical bar of radius 'a' and con-centric thin cylindrical shell of radius 'b' filled in b/w with an electrolyte of resistivity \rho. If the battery is connected to a resistance R, the maximum joule heating in R will take place for
Option: 1 R=\frac{\rho }{2\pi l}\left ( \frac{b}{a} \right )
 
Option: 2 R=\frac{\rho }{2\pi l}\; ln\; \left ( \frac{b}{a} \right )
Option: 3 R=\frac{\rho }{\pi l}\; ln\; \left ( \frac{b}{a} \right )  
Option: 4 R=\frac{2\rho }{\pi l}\; ln\; \left ( \frac{b}{a} \right )

Answers (1)

For maximum power lost or maximum joule heating

Internal Resistance= External Resistance

d R= \frac{\rho \ d r}{2 \pi r l}

R=\text{Internal resistance}=\int d R= \rho \int_{a}^{b} \frac{d r}{2 \pi r l}=\frac{\rho}{2 \pi l} \ln \left(\frac{b}{a}\right)

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