If only ( I^ th 51 ) of the main current is to be passed through a galvanometer then the shunt required is (R₁ ) and if only ( 1^ th 11 ) of the main voltage is to be developed across the galvanometer, then the resistance required (R₂ ). Then ( R₂ R₁ )

Step-by-step solution

According to the question, Case I If only ( 1 51 ) th of the main current (i ) is to be passed through galvanometer (G ) then the shunt required is main current, (i=51 ) ( aligned & i_g=1 & R₁= G i-i_g R₁= G 51-1 = G 50 .(i) aligned ) Case II If only ( 1 11 ) th of the main voltage is developed across the (G ) then the resistance required, (R₂ ). ( aligned & R₂=G (V_G-1 ) & R₂=G(11-1)=10 G (ii) aligned ) Now, from Eqn. (i) and (ii), we get ( aligned & R₂ R₁ = 10 G G 50 =500 & R₂ R₁ =500 aligned )