The resistance of galvanometer is g ohm and the range is 1 volt. The value of resistance used to convert it into a voltmeter of ragne 10 volt is:-

Options

A. 9G
B. G
C. `(1)/(9)G`
D. `10G`

Answer

To convert a galvanometer into a voltmeter, we need to add a series resistance to it. The formula to calculate the required resistance \( R \) for a voltmeter is given by:

\[ R = \frac{V}{I} - g \]

where:
- \( V \) is the maximum voltage range of the voltmeter,
- \( I \) is the current through the galvanometer when the maximum voltage is applied,
- \( g \) is the resistance of the galvanometer.

### Step-by-Step Solution:

1. **Identify the given values:**
- The resistance of the galvanometer \( g \) (in ohms).
- The maximum range of the galvanometer is 1 volt.
- The desired range of the voltmeter is 10 volts.

2. **Calculate the current through the galvanometer:**
The current \( I \) when the galvanometer is at its full scale (1 volt) can be calculated using Ohm's Law:
\[ I = \frac{V_g}{g} = \frac{1}{g} \]
where \( V_g \) is the voltage across the galvanometer.

3. **Substitute the values into the resistance formula:**
Now, we substitute \( V = 10 \) volts (the desired range) and \( I = \frac{1}{g} \) into the formula for \( R \):
\[ R = \frac{10}{\frac{1}{g}} - g \]

4. **Simplify the equation:**
\[ R = 10g - g = 9g \]

5. **Conclusion:**
The value of the resistance used to convert the galvanometer into a voltmeter of range 10 volts is:
\[ R = 9g \]

### Final Answer:
The required resistance is \( 9g \) ohms.