Question

When a resistance of \(200\,\Omega\) is connected in series with a galvanometer of resistance G, its range is V. To triple its range, a resistance of \(2000\,\Omega\) is connected in series. The value of G is

• A. \(400\,\Omega\)
• B. \(500\,\Omega\)
• C. \(700\,\Omega\)
• D. \(900\,\Omega\)

Hint:

Full scale current is fixed, so range is proportional to total resistance.

Answer 1

The Correct Option is C

Step 1: Full scale current:
$I_g$ is the same both times.

Step 2: Ratio of totals:
Total resistance is $G+2000$ in the second case and $G+200$ in the first, and the ratio equals the voltage ratio 3.

Step 3: Solve:
$G+2000=3G+600$, so $G=700$. Option (C).

Final Answer:
The total resistance triples when the range triples. \[ \boxed{C} \]