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: Understanding the Concept:
To make a voltmeter, a high resistance is connected in series with a galvanometer. At full-scale deflection the current is \(I_g\), so the range is \(V=I_g(G+R)\).

Step 2: First case:
\(V=I_g(G+200)\).

Step 3: Second case:
For triple range, \(3V=I_g(G+2000)\).

Step 4: Divide:
\[ 3=\frac{G+2000}{G+200}\ \Rightarrow\ 3G+600=G+2000\ \Rightarrow\ 2G=1400 \]
\[ G=700\ \Omega \]

Step 5: Choose:
Option (C).

Final Answer:
The galvanometer resistance is 700 ohm. \[ \boxed{700\ \Omega} \]