A torch battery of length 
is modelled as a thin solid cylindrical bar (inner electrode) of radius 
coaxial with a thin cylindrical shell (outer electrode) of inner radius 
. The region between them is filled with an electrolyte of resistivity 
(see figure). The battery is connected to an external resistance 
. The value of 
for which the heating in the external resistor is maximum is:
Text Solution
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Consider a thin cylindrical shell at radius 
of thickness 
and length 
. Current flows radially, so the cross-sectional area for radial current at radius 
is
The resistance of that shell is
Integrate from 
to 
Maximum power transfer to the external resistor occurs when the external resistance equals the internal resistance:
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