Question

The range of the voltmeter is \( V \) when \( 50 \, \Omega \) resistance is connected in series. Its range gets doubled when \( 500 \, \Omega \) resistance is connected in series. The resistance of the voltmeter is

• A. 200 \(\Omega\)
• B. 400 \(\Omega\)
• C. 600 \(\Omega\)
• D. 800 \(\Omega\)

Hint:

When the series resistance changes, the range of the voltmeter changes proportionally according to the internal resistance of the voltmeter.

Answer 1

The Correct Option is B

Step 1: Formula for range of voltmeter.
The range of a voltmeter is determined by its internal resistance and the resistance connected in series. If \( R_v \) is the resistance of the voltmeter and \( R_s \) is the series resistance, the total range is given by: \[ \text{Range} = V \times \frac{R_s + R_v}{R_s} \] Step 2: Given conditions.
- When \( R_s = 50 \, \Omega \), the range is \( V \). - When \( R_s = 500 \, \Omega \), the range becomes \( 2V \). Using the equation for the range, we can set up the following ratios: \[ \frac{R_s + R_v}{R_s} = 1 \quad \text{and} \quad \frac{R_s + R_v}{R_s} = 2 \] Solving these equations gives: \[ R_v = 400 \, \Omega \] Step 3: Conclusion.
Thus, the resistance of the voltmeter is \( 400 \, \Omega \), which corresponds to option (B).