A millivoltmeter of 25 m V range is to be converted into an ammeter of 25 A 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 using a shunt resistor, we can follow these steps:

### Step 1: Understand the Circuit Configuration
We need to connect a shunt resistor (Rs) in parallel with the galvanometer (G) of the millivoltmeter. The total current (I) flowing through the circuit will split between the galvanometer and the shunt resistor.

**Hint:** Remember that in a parallel circuit, the voltage across both components is the same.

### Step 2: Identify Given Values
From the problem statement, we know:
- The range of the millivoltmeter (Vg) = 25 mV = 0.025 V
- The desired range of the ammeter (I) = 25 A

**Hint:** Convert all units to standard SI units for consistency.

### Step 3: Define the Current Through the Galvanometer
Let Ig be the current through the galvanometer. The current through the shunt resistor (Is) can be expressed as:
\[ Is = I - Ig \]
Where:
- I = Total current (25 A)
- Ig = Current through the galvanometer

**Hint:** The current through the galvanometer is a fraction of the total current.

### Step 4: Apply Ohm's Law
Using Ohm's law, we can express the voltage across the galvanometer as:
\[ Vg = Ig \cdot Rg \]
Where Rg is the resistance of the galvanometer. Since we are considering an ideal voltmeter, we assume Rg is very high (approaching infinity), making Ig very small.

**Hint:** In an ideal scenario, the resistance of the galvanometer is considered infinite.

### Step 5: Calculate the Shunt Resistance
The voltage across the shunt resistor (Vs) is equal to the voltage across the galvanometer (Vg). Therefore, we can write:
\[ Vg = Is \cdot Rs \]
Substituting Is from Step 3:
\[ Vg = (I - Ig) \cdot Rs \]

Now, rearranging for Rs gives:
\[ Rs = \frac{Vg}{I - Ig} \]

**Hint:** You can substitute Ig as \( \frac{Vg}{Rg} \) if you have the value of Rg, but for an ideal case, Ig is approximately zero.

### Step 6: Substitute Known Values
Substituting the known values:
- Vg = 0.025 V
- I = 25 A
- Ig ≈ 0 (since Rg is infinite)

Thus:
\[ Rs = \frac{0.025}{25 - 0} = \frac{0.025}{25} = 0.001 \, \text{Ohm} \]

### Final Answer
The value of the necessary shunt resistor (Rs) is:
\[ Rs = 0.001 \, \text{Ohm} \]

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