Galvanometer of resistance `25Omega` shows full deflection for current of 10 mA. The resistance required to convert it into 100 V range will be

Options

A. `9975Omega` in series
B. `975Omega` in series
C. `10025Omega` in parallel
D. `10000Omega` in parallel

Explanation

To solve the problem of converting a galvanometer into a voltmeter with a specified range, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Resistance of the galvanometer, \( R_g = 25 \, \Omega \)
- Full deflection current of the galvanometer, \( I_g = 10 \, \text{mA} = 10 \times 10^{-3} \, \text{A} \)
- Desired voltage range, \( V = 100 \, \text{V} \)

2. **Understand the Concept**:
- To convert a galvanometer into a voltmeter, we need to add a series resistance \( R \) to limit the current through the galvanometer to its full-scale deflection current \( I_g \) when the voltmeter is connected across a voltage \( V \).

3. **Use the Formula**:
- The total voltage across the galvanometer and the series resistance can be expressed as:
\[ V = I_g (R + R_g) \]
- Rearranging this gives us:
\[ R = \frac{V}{I_g} - R_g \]

4. **Substitute the Values**:
- Substitute \( V = 100 \, \text{V} \) and \( I_g = 10 \times 10^{-3} \, \text{A} \) into the formula:
\[ R = \frac{100}{10 \times 10^{-3}} - 25 \]

5. **Calculate the Resistance**:
- First, calculate \( \frac{100}{10 \times 10^{-3}} \):
\[ \frac{100}{10 \times 10^{-3}} = \frac{100}{0.01} = 10000 \, \Omega \]
- Now, subtract \( R_g \):
\[ R = 10000 - 25 = 9975 \, \Omega \]

6. **Conclusion**:
- The resistance required to convert the galvanometer into a 100 V range voltmeter is \( R = 9975 \, \Omega \).

### Final Answer:
The required resistance is \( 9975 \, \Omega \).

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