Discussion
The current through a galvanometer of resistance 50 Ω is only 4% of the main current when a shunt resistance is connected. The value of the shunt resistance is approximately
Answer: E
The shunt resistance is approximately \(2\Omega\).
The galvanometer and the shunt are in parallel, so they have the same voltage across them. If the galvanometer carries 4% of the main current, the shunt carries 96%:
\[ \begin{aligned} I_{g}G &= (I - I_{g})S \\ 0.04I \times 50 &= 0.96I \times S \\ S &= \frac{2}{0.96} \approx 2.08\ \Omega \end{aligned} \]
So the shunt is about 2 \(\Omega\). Taking the shunt current as the full current \(I\) instead of 96% of it gives exactly 2 \(\Omega\) as well, which is why the answer is stated as approximate.
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