When a galvanometer is shunted by a resistance ' S ', its current capacity increases ' $n$ ' times. If the…

When a galvanometer is shunted by a resistance ' S ', its current capacity increases ' $n$ ' times. If the same galvanometer is shunted by another resistance $\mathrm{S}^{\prime}$, its current capacity increases to $\mathrm{n}^{\prime}$. The value of $n^{\prime}$ in terms of $n, S$ and $S^{\prime}$ is
  1. $\frac{\mathrm{n}+\mathrm{S}}{\mathrm{S}^{\prime}}$
  2. $\frac{\mathrm{S}(\mathrm{n}-1)-\mathrm{S}^{\prime}}{\mathrm{S}^{\prime}}$
  3. $\frac{(\mathrm{n}+1) \mathrm{S}}{\mathrm{S}^{\prime}}$
  4. $\frac{\mathrm{S}(\mathrm{n}-1)+\mathrm{S}^{\prime}}{\mathrm{S}^{\prime}}$

Solution

From the given data, we can write $\begin{array}{ll} & S=\frac{G}{n-1} \text { and } S^{\prime}=\frac{G}{n^{\prime}-1} \\ \therefore \quad & \frac{S}{S^{\prime}}=\frac{n^{\prime}-1}{n-1} \\ \therefore \quad & S_n-S=S^{\prime} n^{\prime}-S^{\prime} \\ \therefore \quad & S^{\prime} n^{\prime}=S n-S+S^{\prime} \\ \therefore & n^{\prime}=\frac{S(n-1)+S^{\prime}}{S^{\prime}} \end{array}$

Asked in: MHT CET 2024 (03 May Shift 2)

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