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A potentiometer wire AB having length L and resistance 12 r is joined to a cell D of emf ε and internal resistance r . A cell C having EMF ε / 2 and internal resistance 3 r is connected. The length AJ , at which the galvanometer, as shown in the figure, shows no deflection is

Options

  1. A5 12 L
  2. B11 24 L
  3. C11 12 L
  4. D13 24 L

Correct answer

D. 13 24 L

Step-by-step solution

Potential difference across AJ = I   R A J , = ε 13 r · 12 r L · x For no current in galvanometer, ε 2 = potential difference across AJ ε 2 = 12 ε 13 L x x = 13L 24

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