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 ‘2a’ filled in between with an electrolyte of resistivity $ρ$ (see figure). If the battery is connected to a resistance of value R, the maximum Joule heating in R will take place for:

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$R = \frac{ρ}{π l} \ln (2)$

$R = \frac{ρ}{2 π} (2)$

$R = \frac{ρ}{2 π l} \ln (2)$

$R = \frac{2 ρ}{π l} \ln (2)$

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Maximum power in external resistance is generated when it is equal to internal resistance of battery i.e. , $P_{R}$
Maximum when $r = R$
The maximum Joule heating in R
Will take place for, the resistance of small element
$d R = \frac{ρ d r}{2 π r l} \Rightarrow \frac{ρ}{2 π r l} \int_{a}^{2 a} \frac{d r}{r} \Rightarrow R = \frac{ρ}{2 π l} \ln \frac{2 a}{a}$
Question Image