When a resistance of 100 is connected in series with a galvanometer of resistance ' G ', its range is ' V '. To double its range, a resistance of 1000 is connected in series. The value of ' G ' is

Step-by-step solution

A galvanometer is converted to a voltmeter by connecting a high resistance in series, with the range given by V = I_g (G + R) where I_g is the full-scale deflection current, G is the galvanometer resistance, and R is the series resistance. For R₁ = 100 and range V , we have: V = I_g (G + 100) For R₂ = 1000 and range 2V , we have: 2V = I_g (G + 1000) Dividing the equations eliminates I_g and V : 2V V = I_g (G + 1000) I_g (G + 100) 2 = G + 1000 G + 100 Solving for G : 2(G + 100) = G + 1000 2G + 200 = G + 1000 G = 800