Question

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

• A. $\frac{G^2}{S + G}$
• B. $\frac{S}{S + G}$
• C. $\frac{S^2}{S + G}$
• D. $\frac{SG}{S + G}$

Answer 1

Answer: (A)

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 $R$,
$R_{0}=R+\frac{G \times S}{G+R} \dots$(i)
Since, it is given that the current should not change.
So, it should be $G$,
$R_{0}=G \dots$(ii)
From Eq. (i) and (ii), we get
$G=R+\frac{G \times S}{G+S} $
$\Rightarrow R=G-\frac{G S}{G+S} $
$\Rightarrow R=\frac{G^{2}}{G+S}$