A galvanometer reads `5*0V` at full scale deflection and is graded according to its resistance per volt at full scale deflection as `5000OmegaV^-1`. (i) How will you convert it into a voltmeter that reads `20V` at full scale deflection? (ii) Will it still be graded `5000OmegaV^-1`? (iii) Will you prefer this voltmeter to one that is graded `2000OmegaV^-1`?

Explanation

To solve the problem step by step, let's break it down according to the parts of the question.

### Given Data:
- Full scale deflection (FSD) of galvanometer (G) = 5 V
- Resistance per volt at full scale deflection = 5000 Ω/V
- Desired full scale deflection for the voltmeter (V) = 20 V

### (i) Converting the galvanometer into a voltmeter that reads 20V at full scale deflection:

1. **Understanding the Current through the Galvanometer**:
- The galvanometer reads 5V at full scale deflection, and it is graded as 5000 Ω/V.
- The current through the galvanometer (Ig) can be calculated using the resistance per volt:
\[ I_g = \frac{1}{5000} \text{ A} \]

2. **Finding the Total Voltage Drop**:
- The total voltage drop across the voltmeter should be 20V.
- The voltage drop across the galvanometer is 5V, so the voltage drop across the series resistor (R) will be:
\[ V_R = V - V_g = 20V - 5V = 15V \]

3. **Calculating the Required Resistance (R)**:
- The resistance needed in series can be calculated using Ohm's law:
\[ V_R = I_g \cdot R \implies R = \frac{V_R}{I_g} \]
- Substituting the values:
\[ R = \frac{15V}{\frac{1}{5000}} = 15 \times 5000 = 75000 \, \Omega \]

### (ii) Will it still be graded 5000 Ω/V?

1. **Calculating Total Resistance**:
- The total resistance of the circuit when the series resistor is added:
\[ R_{total} = R_g + R = 5000 \, \Omega + 75000 \, \Omega = 80000 \, \Omega \]

2. **Finding the New Resistance per Volt**:
- The new resistance per volt can be calculated as:
\[ \text{Resistance per volt} = \frac{R_{total}}{V} = \frac{80000 \, \Omega}{20V} = 4000 \, \Omega/V \]

3. **Conclusion**:
- Therefore, it will **not** be graded 5000 Ω/V anymore; it will be graded 4000 Ω/V.

### (iii) Will you prefer this voltmeter to one that is graded 2000 Ω/V?

1. **Comparing Current Draw**:
- The current drawn by the voltmeter graded 5000 Ω/V:
\[ I_{5000} = \frac{1}{5000} \text{ A} \]
- The current drawn by the voltmeter graded 2000 Ω/V:
\[ I_{2000} = \frac{1}{2000} \text{ A} \]

2. **Conclusion**:
- Since the voltmeter with 5000 Ω/V draws less current than the one with 2000 Ω/V, it is preferable to use the voltmeter graded 5000 Ω/V.

### Final Answers:
(i) Add a resistance of 75000 Ω in series to convert the galvanometer into a voltmeter that reads 20V at full scale deflection.
(ii) No, it will be graded 4000 Ω/V.
(iii) Yes, the voltmeter graded 5000 Ω/V is preferable as it draws less current.