A galavanometer, whose resistance is 50 ohm has 25 divisions in it. When a current of `4xx10^(-4)` A passes through it,its needle (pointer) deflects by one division. To use this galvanometer as a volmeter of range `2.5V`, it is should be connected to a resistance of :

Options

A. 250 ohm
B. 200 ohm
C. 6200 ohm
D. 6250 ohm

Explanation

To solve the problem of determining the resistance needed to convert a galvanometer into a voltmeter with a range of 2.5V, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Galvanometer's Specifications**:
- The resistance of the galvanometer (Rg) = 50 ohms.
- The galvanometer has 25 divisions.
- A current of \(4 \times 10^{-4}\) A causes a deflection of 1 division.

2. **Calculate the Maximum Current (Imax)**:
- The maximum current that causes full-scale deflection (25 divisions) can be calculated as:
\[ I_{max} = 25 \times (4 \times 10^{-4}) = 10^{-2} \text{ A} = 0.01 \text{ A} \]

3. **Determine the Maximum Voltage (Vmax)**:
- The maximum voltage across the galvanometer when the maximum current flows through it can be calculated using Ohm's Law:
\[ V_{g} = I_{max} \times R_{g} = 0.01 \text{ A} \times 50 \text{ ohms} = 0.5 \text{ V} \]

4. **Calculate the Total Voltage for the Voltmeter**:
- We want the voltmeter to read up to 2.5 V. Therefore, the total voltage (V) across the galvanometer and the series resistance (Rs) needs to be:
\[ V = 2.5 \text{ V} \]

5. **Using Ohm's Law for the Total Circuit**:
- The total voltage can be expressed as:
\[ V = I_{max} \times (R_{g} + R_s) \]
- Rearranging gives:
\[ R_s = \frac{V}{I_{max}} - R_{g} \]

6. **Substituting the Values**:
- Substitute \(V = 2.5 \text{ V}\) and \(I_{max} = 0.01 \text{ A}\):
\[ R_s = \frac{2.5}{0.01} - 50 \]
\[ R_s = 250 - 50 = 200 \text{ ohms} \]

7. **Conclusion**:
- The resistance that should be connected in series with the galvanometer to convert it into a voltmeter of range 2.5 V is **200 ohms**.

### Final Answer:
The galvanometer should be connected to a resistance of **200 ohms**.

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