A galvanometer of resistance `25 Omega` gives full scale deflection for a current of 10 milliampere , is to be changed into a voltmeter of range 100 V by connecting a resistance of ‘ R ’ in series with galvanometer. The value of resistance R in `Omega` is

Options

A. 10000
B. 10025
C. 975
D. 9975

Answer

To solve the problem of converting a galvanometer into a voltmeter, we need to determine the value of the resistance \( R \) that should be connected in series with the galvanometer.

### Step-by-Step Solution:

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

2. **Use Ohm's Law**:
The voltage across the entire circuit (galvanometer + series resistance) when the maximum current flows can be expressed as:
\[ V = I \times R_{\text{total}} \]
where \( R_{\text{total}} = R + R_g \).

3. **Substituting the Known Values**:
We can substitute the known values into the equation:
\[ 100 \, \text{V} = (10 \times 10^{-3} \, \text{A}) \times (R + 25 \, \Omega) \]

4. **Rearranging the Equation**:
Rearranging gives us:
\[ R + 25 = \frac{100}{10 \times 10^{-3}} \]
Simplifying the right side:
\[ R + 25 = \frac{100}{0.01} = 10000 \, \Omega \]

5. **Solving for R**:
Now, isolate \( R \):
\[ R = 10000 - 25 = 9975 \, \Omega \]

6. **Conclusion**:
The value of the resistance \( R \) that needs to be connected in series with the galvanometer is:
\[ R = 9975 \, \Omega \]

### Final Answer:
The value of resistance \( R \) is \( 9975 \, \Omega \).

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