A milli voltmeter of 25 milli volt range is to be converted into an ammeter of 25 ampere range. The value (in ohm) of necessary shunt will be

Options

A. 0.05 Ω
B. 0.001 Ω
C. 0.01 Ω
D. 1 Ω

Explanation

To convert a millivolt meter with a range of 25 millivolts into an ammeter with a range of 25 amperes, we need to calculate the value of the necessary shunt resistor (S) that should be connected in parallel with the voltmeter.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Maximum voltage of the voltmeter (Vg) = 25 mV = 25 × 10^(-3) V
- Maximum current of the ammeter (Im) = 25 A
- The resistance of the voltmeter (R) is unknown.

2. **Calculate the Current through the Voltmeter (Ig):**
- The current through the voltmeter when it reads its maximum voltage can be calculated using Ohm's Law:
\[ I_g = \frac{V_g}{R} \]
- Here, \(V_g = 25 \times 10^{-3} \, \text{V}\).

3. **Determine the Total Current (Im) and the Current through the Shunt (Is):**
- The total current flowing through the circuit when the ammeter is at maximum is \(I_m = 25 \, \text{A}\).
- The current through the shunt resistor (Is) can be expressed as:
\[ I_s = I_m - I_g \]

4. **Apply Kirchhoff's Voltage Law:**
- The voltage across the voltmeter (Vg) is equal to the voltage across the shunt resistor (Vs):
\[ V_g = I_g \cdot R = I_s \cdot S \]
- This leads to:
\[ I_g \cdot R = (I_m - I_g) \cdot S \]

5. **Rearranging the Equation to Solve for S:**
- From the above equation, we can rearrange to find S:
\[ S = \frac{I_g \cdot R}{I_m - I_g} \]

6. **Substituting the Values:**
- We know \(I_g = \frac{25 \times 10^{-3}}{R}\).
- Substitute \(I_g\) into the equation for S:
\[ S = \frac{\left(\frac{25 \times 10^{-3}}{R}\right) \cdot R}{25 - \frac{25 \times 10^{-3}}{R}} \]
- This simplifies to:
\[ S = \frac{25 \times 10^{-3}}{25 - 25 \times 10^{-3}/R} \]

7. **Assuming R is Large:**
- Since R is much larger than the shunt resistance S, we can approximate:
\[ S \approx \frac{25 \times 10^{-3}}{25} = 10^{-3} \, \text{ohm} \]

8. **Final Calculation:**
- Thus, the value of the necessary shunt resistor (S) is:
\[ S = 0.001 \, \text{ohm} \]

### Conclusion:
The value of the necessary shunt resistor is **0.001 ohm**.