Question

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 :

• A. $R =\frac{2 \rho}{\pi l} \ln \left(\frac{ b }{ a }\right)$
• 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. $R =\frac{\rho}{2 \pi l} \ln \left(\frac{ b }{ a }\right)$

Answer 1

Answer: (D)

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

Answer 2

Maximum power in external resistance is generated when it is equal to internal resistance of battery.