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 ONLINE 09-04-2016]

A) 2S = G

B) 2G = S

C) S(R+G) = RG

D) 2S(R+G) = RG

Correct Answer: C

Solution :

[c] 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