A galvanometer with a coil of resistance `12.0Omega` shows full scale deflection for a current `2*5mA`. How will you convert the meter into (i) an ammeter of range 0 to `7*5A` (b) a voltmeter of range 0 to 10V.

Explanation

To solve the problem of converting a galvanometer into an ammeter and a voltmeter, we will follow these steps:

### Given Data:
- Resistance of the galvanometer (G) = 12.0 Ω
- Full-scale deflection current of the galvanometer (Ig) = 2.5 mA = 2.5 × 10^(-3) A
- Desired range of the ammeter (I) = 7.5 A
- Desired range of the voltmeter (V) = 10 V

### Part (i): Converting the galvanometer into an ammeter

1. **Calculate the Shunt Resistance (Rs)**:
The shunt resistance is used in parallel with the galvanometer to allow most of the current to bypass the galvanometer. The formula for shunt resistance is given by:
\[ R_s = \frac{I_g \cdot G}{I - I_g} \]
Where:
- \(I_g\) = full-scale deflection current of the galvanometer
- \(G\) = resistance of the galvanometer
- \(I\) = total current through the ammeter

2. **Substituting the Values**:
\[ R_s = \frac{(2.5 \times 10^{-3}) \cdot 12}{7.5 - 2.5 \times 10^{-3}} \]
\[ R_s = \frac{(2.5 \times 12) \times 10^{-3}}{7.5 - 0.0025} \]
\[ R_s = \frac{30 \times 10^{-3}}{7.4975} \]

3. **Calculating Rs**:
\[ R_s \approx \frac{30 \times 10^{-3}}{7.4975} \approx 0.0040 \, \Omega \]

### Part (ii): Converting the galvanometer into a voltmeter

1. **Calculate the Series Resistance (R)**:
To convert the galvanometer into a voltmeter, we need to add a resistance in series. The formula for the series resistance is:
\[ R = \frac{V}{I_g} - G \]
Where:
- \(V\) = desired voltage range
- \(I_g\) = full-scale deflection current of the galvanometer
- \(G\) = resistance of the galvanometer

2. **Substituting the Values**:
\[ R = \frac{10}{2.5 \times 10^{-3}} - 12 \]
\[ R = 4000 - 12 \]
\[ R = 3988 \, \Omega \]

### Summary of Results:
- **Shunt Resistance for Ammeter**: \(R_s \approx 0.0040 \, \Omega\)
- **Series Resistance for Voltmeter**: \(R \approx 3988 \, \Omega\)