A galvanometer is to be converted into an ammeter or voltmeter. In which of the following cases the resistance of the device is largest?

Options

A. an ammeter of range `10A`
B. a voltmeter of range `5V`
C. an ammeter of range `5A`
D. a voltmeter of range `10V`

Explanation

To determine in which case the resistance of the device is largest when converting a galvanometer into an ammeter or voltmeter, we can analyze the configurations used for each conversion.

### Step-by-Step Solution:

1. **Understand the Galvanometer**:
- A galvanometer has a certain internal resistance, denoted as \( R_G \).

2. **Conversion to Ammeter**:
- To convert a galvanometer into an ammeter, a shunt resistance \( R_S \) is connected in parallel with the galvanometer.
- The equivalent resistance \( R_A \) of the ammeter can be calculated using the formula for resistors in parallel:
\[ R_A = \frac{R_G \cdot R_S}{R_G + R_S} \]
- Since \( R_A \) is the result of a parallel combination, it will always be less than \( R_G \) (the resistance of the galvanometer).

3. **Conversion to Voltmeter**:
- To convert a galvanometer into a voltmeter, a series resistance \( R_S' \) is connected in series with the galvanometer.
- The total resistance \( R_V \) of the voltmeter is given by:
\[ R_V = R_G + R_S' \]
- In this case, \( R_V \) will always be greater than \( R_G \) because you are adding another resistance in series.

4. **Comparison of Resistances**:
- From the above calculations, we can conclude:
- The resistance of the ammeter \( R_A \) is less than \( R_G \).
- The resistance of the voltmeter \( R_V \) is greater than \( R_G \).
- Therefore, the resistance of the device is largest when the galvanometer is converted into a voltmeter.

5. **Conclusion**:
- The device with the largest resistance is the voltmeter.