With a resistance ' X ' connected in series with a galvanometer of resistance 100 , it acts as a voltmeter of range 0 - 15 V. To double the range, a resistance of 1500 is to be connected in series with ' X '. The value of ' X ' in is

Step-by-step solution

Let I_g be the full-scale deflection current of the galvanometer. For the initial voltmeter of range 15 V : V₁ = I_g(G + X) 15 = I_g(100 + X) When the range is doubled to 30 V , an additional resistance of 1500 is connected in series: V₂ = I_g(G + X + 1500) 30 = I_g(100 + X + 1500) 30 = I_g(1600 + X) Dividing the second equation by the first equation: 30 15 = 1600 + X 100 + X 2 = 1600 + X 100 + X 200 + 2X = 1600 + X X = 1400 Answer: 1400