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JEE Main 2022 (30 Jul, Shift 2) · Cells: EMF, Internal Resistance & Combinations

Cells: EMF, Internal Resistance & Combinations question from JEE Main 2022 (30 Jul, Shift 2)

Q24JEE Main 2022 · 30 JUL · SHIFT 2Medium

Cells: EMF, Internal Resistance & Combinations

A cell sends a current through a resistance 4 Ω4\ \Omega for time tt and sends current through another resistance 16 Ω16\ \Omega for the same time tt. If the same amount of heat is developed in both the resistances, then the internal resistance of the cell is _____ Ω\Omega

Numerical answer type. Work it out, then open the answer.

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Answer: 8

  1. Heat =I2Rt=E2R(R+r)2t= I^2Rt = \dfrac{E^2R}{(R + r)^2}t; equal heat for R1R_1 and R2R_2 gives r=R1R2r = \sqrt{R_1R_2}.
  2. 4(4+r)2=16(16+r)2⇒16+r=2(4+r)\dfrac{4}{(4 + r)^2} = \dfrac{16}{(16 + r)^2} \Rightarrow 16 + r = 2(4 + r)
  3. r=4×16=8 Ωr = \sqrt{4 \times 16} = 8\ \Omega
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