A teacher in his physics laboratory allotted an experiment to determine the resistance $(G)$ of a galvanometer. Students took the observations for $\frac{1}{3}$ deflection in the galvanometer. Which of the below is true for measuring value of $G$ $?$
A$\frac{1}{3}$ deflection method cannot be used for determining the resistance of the galvanometer.
B$\frac{1}{3}$ deflection method can be used and in this case the $G$ equals to twice the value of shunt resistance$(s).$
C$\frac{1}{3}$ deflection method can be used and in this case, the $G$ equals to three times the value of shunt resistance$(s)$
D$\frac{1}{3}$ deflection method can be used and in this case the $G$ value equals to the shunt resistance$(s).$
JEE MAIN 2022, Diffcult
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B$\frac{1}{3}$ deflection method can be used and in this case the $G$ equals to twice the value of shunt resistance$(s).$
b $\Rightarrow\left( I - I _{ g }\right) S = I _{ g } G$
$\frac{I_{g}}{I}=\frac{S}{S+G}$
$\Rightarrow \frac{1}{3}=\frac{S}{S+G} \Rightarrow S+G=3 S \Rightarrow G=2 S$
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