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A galvanometer of resistance $50 \Omega$ is converted to an ammeter. After shunting, the effective resistance of ammeter is $2.5 \Omega$. The value of shunt is
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Verified Answer
The correct answer is:
$\frac{50}{19} \Omega$
The resistance of the galvanometer and the shunt are in parallel. Their equivalent resistance is given by
$$
\begin{aligned}
& \frac{1}{\mathrm{R}}=\frac{1}{\mathrm{G}}+\frac{1}{\mathrm{~S}} \\
& \therefore \frac{1}{\mathrm{~S}}=\frac{1}{2.5}-\frac{1}{50}=\frac{19}{50}
\end{aligned}
$$
Or $\mathrm{S}=\frac{50}{19} \Omega$
$$
\begin{aligned}
& \frac{1}{\mathrm{R}}=\frac{1}{\mathrm{G}}+\frac{1}{\mathrm{~S}} \\
& \therefore \frac{1}{\mathrm{~S}}=\frac{1}{2.5}-\frac{1}{50}=\frac{19}{50}
\end{aligned}
$$
Or $\mathrm{S}=\frac{50}{19} \Omega$
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