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 ohm is

Step-by-step solution

Converting a galvanometer to a voltmeter requires a series resistance R_s such that the voltmeter range is V = I_g (R_g + R_s) , with I_g as the full-scale deflection current, R_g the galvanometer resistance, and R_s the series resistance. For a 15 V range with R_g = 100 and series resistance X , 15 = I_g (100 + X) Doubling the range to 30 V requires an additional 1500 in series, making the total series resistance X + 1500 . 30 = I_g (100 + X + 1500) = I_g (1600 + X) Dividing this equation by the first yields 30 15