Question

How do you calculate the shunt required to increase the length small n times?

Answer 1

1. In the arrangement as shown in the figure, I and I_g are the current through the circuit and galvanometer respectively.
   Therefore, the current through shunt S is, I_s = (I – I_g)
   
2. Since S and G are parallel, the potential difference across them is the same.
   ∴ GI_g = S I_s
   ∴ GI_g = S (I - I_g) 
   ∴ S = `(("I"_"g")/("I" - "I"_"g"))"G"` ….(1)
   Equation (1) is useful to calculate the range of current that the galvanometer can measure.
3. If the current I is n times current I_g, then I = n I_g. Using this in equation (1), 
   S = `(("G""I"_"g")/("n""I"_"g" - "I"_"g"))`
   ∴ S = `"G"/("n" - 1)`
   This is the required shunt to increase the range n times.