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JEE MainPhysicsCurrent Electricity

A galvanometer of resistance 45 shows full scale deflection for a current of 2 mA. It is converted into an ammeter of range 20 mA by connecting a suitable shunt resistance. This newly formed ammeter is then connected in series with an ideal battery of emf 1.5 V and an unknown external resistor R . If the ammeter shows full scale deflection in the circuit, the value of R is

Options

  1. A30.0
  2. B70.0
  3. C70.5
  4. D75.0

Correct answer

C. 70.5

Step-by-step solution

First, we find the shunt resistance S required to convert the galvanometer into the ammeter. Given: Galvanometer resistance, G = 45 Full scale deflection current of galvanometer, I_g = 2 mA Range of ammeter, I = 20 mA Using the current division principle: I_g G = (I - I_g) S 2 45 = (20 - 2) S 90 = 18 S S = 5 The equivalent resistance of the ammeter R_A is the parallel combination of G and S : R_A = G S G + S = 45 5 45 + 5 = 225 50 = 4.5 When connected in the circuit, the ammeter shows full scale deflection, meaning

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