question_answer

To know the resistance G of a galvanometer by half deflection method, a battery of emf \[{{V}_{E}}\] and resistance R is used to deflect the galvanometer by angle\[\theta .\]If a shunt of resistance S is needed to gat half deflection then G, R and S are related by the equation :   JEE Main Online Paper (Held On 09 April 2016)

A) 2S = G                                  

B) 2G = S                

C) S(R+G) = RG                      

D) 2S(R+G) = RG

Correct Answer: C

Solution :

  Case-1                                  Case-2 \[{{i}_{1}}=\frac{{{V}_{E}}}{R+G}\]                           \[i=\frac{{{V}_{E}}}{R+\frac{GS}{G+S}}\] \[\frac{{{i}_{1}}}{2}G=\left( i-\frac{{{i}_{1}}}{2} \right)S\]               \[{{i}_{1}}(G+S)=2iS\] substituting \[{{i}_{1}}\] and i we get S(R+G) = RG