A galvanometer coil has a resistance of `10Omega` and the metre show full scale deflection for a current of 3 mA. The galvanometer will be converted into voltmeter by:

Options

A. connecting a resistance in series
B. connecting a resistance in parallel
C. connecting a shunt wire
D. by connecting a battery

Explanation

To convert a galvanometer into a voltmeter, we need to follow these steps:

### Step-by-Step Solution:

1. **Understand the Galvanometer Specifications**:
- The galvanometer has a resistance (\( R_g \)) of \( 10 \, \Omega \).
- It shows full-scale deflection (FSD) for a current (\( I_g \)) of \( 3 \, \text{mA} \) or \( 0.003 \, \text{A} \).

2. **Determine the Voltage at Full Scale Deflection**:
- The voltage (\( V_g \)) across the galvanometer at full-scale deflection can be calculated using Ohm's Law:
\[ V_g = I_g \times R_g \]
- Substituting the values:
\[ V_g = 0.003 \, \text{A} \times 10 \, \Omega = 0.03 \, \text{V} \, \text{or} \, 30 \, \text{mV} \]

3. **Convert the Galvanometer into a Voltmeter**:
- To convert the galvanometer into a voltmeter, we need to add a resistor (\( R \)) in series with the galvanometer. This resistor will allow the voltmeter to measure higher voltages without exceeding the full-scale deflection of the galvanometer.
- The total resistance of the voltmeter (\( R_v \)) will be:
\[ R_v = R_g + R \]

4. **Determine the Required Series Resistance**:
- If we want the voltmeter to measure a certain voltage (\( V \)), we can use Ohm's Law again:
\[ V = I_g \times R_v \]
- Rearranging gives:
\[ R_v = \frac{V}{I_g} \]
- Therefore, the series resistance needed can be calculated as:
\[ R = R_v - R_g \]

5. **Conclusion**:
- To convert the galvanometer into a voltmeter, connect a suitable resistor in series with the galvanometer. This will allow the device to measure higher voltages while ensuring that the current through the galvanometer does not exceed \( 3 \, \text{mA} \).