Question 345 of 380

A teacher in his physics laboratory allotted an experiment to determine the resistance $\left(G\right)$ a galvanometer. Students took the observations for $\dfrac{1}{3}$ deflection in the galvanometer. Which of the below is true for measuring value of $G$?

A$\dfrac{1}{3}$ deflection method cannot be used for determining the resistance of the galvanometer.B$\dfrac{1}{3}$ deflection method can be used and in this case the $G$ equals to twice the value of shunt resistance(s).C$\dfrac{1}{3}$ deflection method can be used and in this case, the G equals to three times the value of shunt resistance(s).D$\dfrac{1}{3}$ deflection method can be used and in this case the $G$ value equals to the shunt resistance(s)

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Answer: (B) $\dfrac{1}{3}$ deflection method can be used and in this case the $G$ equals to twice the value of shunt resistance(s).

If a large resistance $R$ is connected with a battery, then current will be approximately $\dfrac{\epsilon }{R}$, and $t$ will remain almost constant.
In ${1}^{st}$ case, only $\left(G\right)$ is connected $\Rightarrow ig=i$
In ${2}^{nd}$ case,
${i}_{g}{R}_{0}=\left(I-{i}_{g}\right)S \Rightarrow {\left({i}_{g}\right)}_{2}=\left(\dfrac{S}{{R}_{g}+S}\right)i$
If ${\left({i}_{g}\right)}_{2}=\dfrac{1}{3}\left({i}_{g}\right),\Rightarrow \left(\dfrac{S}{{R}_{g}+S}\right)i=\dfrac{1}{3}i$
${R}_{g}=2S$