Verified Solution • 2025–26 Session moderate

QJEEM20Phd1f4: JEE Main 2020 Physics - Class 12 JEEM20Phd1f4 Solution: Model a torch battery of length to be made up of a thin…

Model a torch battery of length ll 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 ρ\rho (see figure). If the battery is connected to a resistance of value R, the maximum Joule heating in R will take place for : JEE Main 2020 (Online) 3rd September Morning Slot Physics - Current Electricity Question 217 English

Multiple Choice Options

  • A R=2ρπlln⁡(ba)R = {{2\rho } \over {\pi l}}\ln \left( {{b \over a}} \right)
  • B R=ρπlln⁡(ba)R = {\rho \over {\pi l}}\ln \left( {{b \over a}} \right)
  • C R=ρ2πlln⁡(ba)R = {\rho \over {2\pi l}}\ln \left( {{b \over a}} \right)
  • D R=ρ2πl(ba)R = {\rho \over {2\pi l}}\left( {{b \over a}} \right)

Step-by-Step Verified Solution

JEE Main 2020 (Online) 3rd September Morning Slot Physics - Current Electricity Question 217 English Explanation

Internal resitance of battery

∫dr=∫abρdr2πrl\int {dr} = \int\limits_a^b {{{\rho dr} \over {2\pi rl}}}

⇒\Rightarrow r = ρ2πlln⁡ba{{\rho \over {2\pi l}}\ln {b \over a}}

Power in external resistance PR = (∈r+R)2R{\left( {{ \in \over {r + R}}} \right)^2}R

Maximum Power in external resistance is generated when it is equal to internal resistance of battery. So PR is maximum when r = R.

∴\therefore R = ρ2πlln⁡ba{{\rho \over {2\pi l}}\ln {b \over a}}

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring