Question

The maximum safe voltage that can be measured using a galvanometer of resistance G is V_m . Find the resistance to be connected in series with the galvanometer so that it becomes a voltmeter of range nV_m. 

Answer 1

1. Let ‘X’ be the resistance connected in series with the galvanometer as shown in the figure.
   
2. If V is the voltage to be measured, then
   V = I_g X + I_g G
   ∴ I_g X = V - I_g G
   ∴ X = `"V"/"I"_"g" - "G"` ….(1)
   where I_g is the current flowing through the galvanometer.
3. If voltage V is n times voltage V_m (voltage across galvanometer) then,
   V = n V_m = n(I_gG) 
   Using this in equation (1),
   ∴ X = `("n""I"_"g""G")/("I"_"g") - "G"`
   ∴ X = G (n - 1)