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Saturday, 31 October

JEE Main 2020 · PhysicsMultiple choiceSingle correctHardMulti-step

JEE Main 3 September 2020, Shift 1, Physics Q12

Question 12 of 75 in this shift, Physics question 12 of 25.

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 :

The figure, in words

A vertical cylinder drawn with a hatched thin central bar and a larger outer cylindrical shell (top edge dashed); the space between is labelled rho; a double-headed vertical arrow on the left is labelled l; below are an arrow labelled a (vector arrow over a) and a longer arrow labelled b pointing to the right.
  1. (1)R = ρ2πl(ba)\frac{\rho}{2\pi l}\left(\frac{b}{a}\right)
  2. (2)R = ρ2πl ln(ba)\frac{\rho}{2\pi l}\, ln\left(\frac{b}{a}\right)Official answer
  3. (3)R = ρπl ln(ba)\frac{\rho}{\pi l}\, ln\left(\frac{b}{a}\right)
  4. (4)R = 2ρπl ln(ba)\frac{2\rho}{\pi l}\, ln\left(\frac{b}{a}\right)

Official answer

Option 2

NTA final key (Sep 2020).

Chapter
Current Electricity
Topic
Ohm's Law and Resistance
Idea tested
Radial Resistance of a Hollow Cylinder

Same topic in other shifts

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. This question needs a figure we do not reproduce; it is described in words above. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.