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. `0.001`
B. `0.01`
C. 1
D. `0.05`

Answer

To convert a millivoltmeter into an ammeter, we need to calculate the value of the necessary shunt resistor. Here’s how we can do it step by step:

### Step 1: Understand the Given Values
- The range of the millivoltmeter (Vg) = 25 mV = 25 × 10^(-3) V
- The desired range of the ammeter (I) = 25 A

### Step 2: Determine the Current through the Galvanometer
Let Ig be the current through the galvanometer (the millivoltmeter). The voltage across the galvanometer can be expressed as:
\[ V_g = I_g \times R_g \]
where Rg is the resistance of the galvanometer.

From the given voltage range:
\[ I_g \times R_g = 25 \times 10^{-3} \]
Thus, we can express Ig as:
\[ I_g = \frac{25 \times 10^{-3}}{R_g} \]

### Step 3: Set Up the Current Division
The total current (I) flowing through the circuit is 25 A. The current through the shunt resistor (Is) can be expressed as:
\[ I_s = I - I_g = 25 - I_g \]

### Step 4: Apply the Voltage Equality
Since the galvanometer and the shunt resistor are in parallel, the voltage across both must be the same:
\[ I_g \times R_g = I_s \times R_s \]
Substituting Is:
\[ I_g \times R_g = (25 - I_g) \times R_s \]

### Step 5: Substitute Ig in the Equation
Now, substitute the expression for Ig:
\[ \left(\frac{25 \times 10^{-3}}{R_g}\right) \times R_g = (25 - \frac{25 \times 10^{-3}}{R_g}) \times R_s \]
This simplifies to:
\[ 25 \times 10^{-3} = (25 - \frac{25 \times 10^{-3}}{R_g}) \times R_s \]

### Step 6: Approximate the Value of Is
Since Rg is typically much larger than the shunt resistance Rs, we can approximate:
\[ 25 - \frac{25 \times 10^{-3}}{R_g} \approx 25 \]
Thus, we can rewrite the equation as:
\[ 25 \times 10^{-3} = 25 \times R_s \]

### Step 7: Solve for Rs
Now, solving for Rs gives:
\[ R_s = \frac{25 \times 10^{-3}}{25} = 10^{-3} \text{ ohms} = 0.001 \text{ ohms} \]

### Conclusion
The value of the necessary shunt resistor is:
\[ R_s = 0.001 \text{ ohms} \]