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NTA Abhyas JEE Main2020PhysicsCurrent ElectricityPractice

Two cells, having the same E.M.F. are connected in series through an external resistance R . Cells have internal resistances r 1 and r 2 r 1 > r 2 respectively. When the circuit is closed, the potential difference across the first cell is zero. The value of R is

Options

  1. Ar 1 + r 2 2
  2. Br 1 - r 2 2
  3. Cr 1 + r 2
  4. Dr 1 - r 2

Correct answer

D. r 1 - r 2

Step-by-step solution

Current in the circuit = E + E r 1 + r 2 + R = 2 E r 1 + r 2 + R Potential difference across first cell = E - ir 1 = E - 2 E × r 1 r 1 + r 2 + R Now, E - 2 Er 1 r 1 + r 2 + R = 0 ⇒ E = 2 Er 1 r 1 + r 2 + R ⇒ 2 r 1 = r 1 + r 2 + R R = r 1 - r 2

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