A moving coil galvanometer of resistance G gives its full scale deflection when a current Ig flows through its - Physics - Moving Charges And Magnetism

Question

A moving coil galvanometer of resistance G gives its full scale
deflection when a current Ig flows through its coil It can be
converted into an ammeter of range ( 0 to I)(I>Ig) when a shunt
resistance S is connected across its coil If this galvanometer is
converted into an ammeter of range 0 to 2I , find the expression
for the shunt required in terms of S and G?
Please help as soon as possible

Roopesh Singh · Accepted Answer

For an ammeter of the range 0 to I we have

$I_{g} G = I_{S} S ...................... (1) I = I_{g} + I_{S} I_{s} = I - I_{g} ................... (2) Substitute (2) in (1): I_{g} G = (I - I_{g}) S \Rightarrow S = [\frac{I_{g}}{I - I_{g}}] G$

Therefore,

$For getting S' for range 0 to 2I, replace I by 2I in this formula. S' = [\frac{I_{g}}{2 I - I_{g}}] G and solve equation of S for I . \frac{(I - I_{g})}{I_{g}} = \frac{G}{S} \Rightarrow I = I_{g} (\frac{G}{S} + 1) \Rightarrow 2 I - I_{g} = {2 I}_{g} (\frac{G}{S}) + I_{g} \frac{I_{g}}{(2 I - I_{g})} = \frac{1}{(2 (\frac{G}{S}) + 1)} \Rightarrow S' = \frac{G S}{2 G + S} S' = \frac{S}{2 + \frac{S}{G}} ans.$