$ ext{A moving coil galvanometer of resistance 50 } \Omega ext{ gives a full scale deflection, when a current of 0.5 mA is passed through it. The resistance required to convert it into a voltmeter of range 10 volt, is :}$

Q: $\text{A moving coil galvanometer of resistance 50 } \Omega \text{ gives a full scale deflection, when a current of 0.5 mA is passed through it. The resistance required to convert it into a voltmeter of range 10 volt, is :}$

$\text{A moving coil galvanometer of resistance 50 } \Omega \text{ gives a full scale deflection, when a current of 0.5 mA is passed through it. The resistance required to convert it into a voltmeter of range 10 volt, is :}$

Question

$	ext{A moving coil galvanometer of resistance 50 } \Omega 	ext{ gives a full scale deflection, when a current of 0.5 mA is passed through it. The resistance required to convert it into a voltmeter of range 10 volt, is :}$

Accepted Answer

To convert a moving coil galvanometer into a voltmeter, we need to add a series resistance to it. The purpose of this series resistance is to ensure that the galvanometer can measure higher voltages without exceeding its full-scale deflection current.

### Given:
- Resistance of the galvanometer, $ R_g = 50 \, \Omega $
- Full-scale deflection current, $ I = 0.5 \, \text{mA} = 0.0005 \, \text{A} $
- Desired voltage range of the voltmeter, $ V = 10 \, \text{V} $

### Calculation:
The formula to calculate the series resistance $ R_s $ required to convert the galvanometer into a voltmeter is:

$$
R_s = \frac{V}{I} - R_g
$$

Substituting the given values:

$$
R_s = \frac{10 \, \text{V}}{0.0005 \, \text{A}} - 50 \, \Omega
$$

$$
R_s = 20000 \, \Omega - 50 \, \Omega
$$

$$
R_s = 19950 \, \Omega
$$

Thus, the resistance required to convert the galvanometer into a voltmeter of range 10 volts is $ 19950 \, \Omega $.

### Explanation of Options:

1. **Option 1: $ 1950 \, \Omega $**
   - This option is incorrect because it does not account for the correct calculation of the series resistance needed. The calculation clearly shows that the resistance required is much higher than $ 1950 \, \Omega $.

2. **Option 2: $ 2000 \, \Omega $**
   - This option is incorrect because it significantly underestimates the required series resistance. The calculation shows that $ 2000 \, \Omega $ is not sufficient to achieve the desired voltage range.

3. **Option 3: $ 19950 \, \Omega $**
   - This is the correct option. The calculation confirms that $ 19950 \, \Omega $ is the precise resistance needed to convert the galvanometer into a voltmeter with a 10-volt range.

4. **Option 4: $ 20000 \, \Omega $**
   - This option is incorrect because it slightly overestimates the required resistance. The correct calculation shows that the resistance should be $ 19950 \, \Omega $, not $ 20000 \, \Omega $.

In conclusion, Option 3 is the correct answer because it accurately reflects the calculated series resistance needed to convert the galvanometer into a voltmeter with the specified range.