A galvanometer of resistance ' $G$ ' is shunted by resistance of 'S' ohm. To keep the main current in the…

A galvanometer of resistance ' $G$ ' is shunted by resistance of 'S' ohm. To keep the main current in the circuit unchanged the resistance to be put in series with Galvanometer is
  1. $\frac{\mathrm{G}^2}{\mathrm{~S}+\mathrm{G}}$
  2. $\frac{\mathrm{G}}{\mathrm{S}+\mathrm{G}}$
  3. $\frac{\mathrm{S}^2}{\mathrm{G}+\mathrm{S}}$
  4. $\frac{\mathrm{GS}}{\mathrm{S}+\mathrm{G}}$

Solution

$\begin{array}{ll} & \text { Now, } \mathrm{G}=\left(\frac{\mathrm{GS}}{\mathrm{S}+\mathrm{G}}\right)+\mathrm{S}^{\prime} \\ \therefore \quad & \mathrm{G}-\frac{\mathrm{GS}}{\mathrm{S}+\mathrm{G}}=\mathrm{S}^{\prime} \\ \therefore \quad & \mathrm{S}^{\prime}=\frac{\mathrm{G}^2}{\mathrm{~S}+\mathrm{G}}\end{array}$

Asked in: MHT CET 2024 (02 May Shift 1)

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