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. \( 700\Omega \)
• B. \( 900\Omega \)
• C. \( 400\Omega \)
• D. \( 600\Omega \)

Hint:

Always compare voltage ranges by dividing equations to eliminate galvanometer current.

Answer 1

The Correct Option is A

Step 1: Voltage range relation.
The voltage range of a galvanometer converted into a voltmeter is \[ V = I_g (G + R) \]
Step 2: Write equations for both cases.
Initial range: \[ V = I_g (G + 200) \] Tripled range: \[ 3V = I_g (G + 2000) \]
Step 3: Divide the equations.
\[ \frac{3V}{V} = \frac{G + 2000}{G + 200} \Rightarrow 3(G + 200) = G + 2000 \]
Step 4: Solve for \( G \).
\[ 3G + 600 = G + 2000 \Rightarrow 2G = 1400 \Rightarrow G = 700\Omega \]
Step 5: Conclusion.
The resistance of the galvanometer is \( 700\Omega \).