A galvanometer of resistance $G \Omega$, is shunted by a resistance $S \Omega$. To keep the main current in…

A galvanometer of resistance $G \Omega$, is shunted by a resistance $S \Omega$. To keep the main current in the circuit unchanged, the resistance to be connected in series with the galvanometer is
  1. $\frac{G^2}{S+G}$
  2. $\frac{S}{S+G}$
  3. $\frac{S^2}{S+G}$
  4. $\frac{S G}{S+G}$

Solution

Given, galvanometer resistance, $R_G=G$ and shunt resistance, $R_S=S$, Let the series resistance is $R$, so the net resistance of circuit after connected $R$,
Since, it is given that the current should not change. So, it should be $G$,
From Eq. (i) and (ii), we get $ \begin{aligned} G & =R+\frac{G \times S}{G+S} \\ \Rightarrow \quad R & =G-\frac{G S}{G+S} \Rightarrow R=\frac{G^2}{G+S} \end{aligned} $ Hence, the correct option is (a)

Asked in: AP EAMCET 2019 (21 Apr Shift 1)

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