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A galvanometer can be converted into an ammeter of range 0.5 A by connecting a shunt of 5 . The same galvanometer can be converted into an ammeter of range 2.3 A by connecting a shunt of 1 . The resistance of the galvanometer is

Options

  1. A45
  2. B50
  3. C40
  4. D55

Correct answer

A. 45

Step-by-step solution

Let I_g be the full-scale deflection current and G be the resistance of the galvanometer. For the first conversion (range I₁ = 0.5 A , shunt S₁ = 5 ): I_g G = (I₁ - I_g) S₁ I_g (G + 5) = 0.5 5 I_g (G + 5) = 2.5 (1) For the second conversion (range I₂ = 2.3 A , shunt S₂ = 1 ): I_g G = (I₂ - I_g) S₂ I_g (G + 1) = 2.3 1 I_g (G + 1) = 2.3 (2) Dividing equation (1) by equation (2) to eliminate I_g : G + 5 G + 1 = 2.5 2.3 Cross-multiplying: 2.3 (G + 5) = 2.5 (G + 1) 2.3 G + 11.5 = 2.5 G + 2.5 Rearranging to solve for G :

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