Two identical moving coil galvanometers have 10 resistance and full-scale deflection at 2 A current. One of them is converted into a voltmeter of range 10 ~mV and the other into an ammeter of range 1 ~mA using appropriate resistors. The ratio of resistance of the converted voltmeter to that of the ammeter is

Step-by-step solution

The resistance of the galvanometer is G = 10 and the full-scale deflection current is I_g = 2 10⁻⁶ A . For the voltmeter, the range is V = 10 mV = 10⁻² V . The total resistance of the voltmeter is R_V = V I_g = 10⁻² 2 10⁻⁶ = 5000 . For the ammeter, the range is I = 1 mA = 10⁻³ A . The shunt resistance S is connected in parallel with G such that I_g G = (I - I_g) S . Thus, S = I_g G I - I_g = 2 10⁻⁶ 10 10⁻³ - 2 10⁻⁶ = 2 10⁻⁵ 0.998 10⁻³ 2 10⁻⁵ 10⁻³ = 0.02 . The total resistance of the ammeter is R_A = G S G + S S = 0