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 resistance in series with the galvanometer. The formula to find the resistance \( R \) required to convert a galvanometer into a voltmeter is given by:

\[ R = \frac{V}{I_g} - G \]

Where:
- \( V \) is the desired voltage range of the voltmeter,
- \( I_g \) is the current through the galvanometer when the full-scale deflection occurs,
- \( G \) is the resistance of the galvanometer.

### Step-by-step Solution:

1. **Identify Given Values:**
- The resistance of the galvanometer \( G \) is given as \( g \) ohms.
- The range of the galvanometer is \( 1 \) volt.
- The desired range of the voltmeter is \( 10 \) volts.

2. **Calculate the Current \( I_g \):**
- The current \( I_g \) when the galvanometer shows full-scale deflection at \( 1 \) volt can be calculated using Ohm's law:
\[ I_g = \frac{V_g}{G} = \frac{1}{g} \]

3. **Substitute Values into the Resistance Formula:**
- Now substitute \( V = 10 \) volts and \( I_g = \frac{1}{g} \) into the resistance formula:
\[ R = \frac{10}{\frac{1}{g}} - g \]

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

5. **Final Result:**
- Therefore, the value of the resistance used to convert the galvanometer into a voltmeter of range \( 10 \) volts is:
\[ R = 9g \text{ ohms} \]

### Final Answer:
The resistance used to convert the galvanometer into a voltmeter of range 10 volts is \( 9g \) ohms.

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