A galvanometer having coil resistance `8Omega` shows a full scale deflection for a current of "3mA" .For it to measure a current of "8A" ,the value of the shunt should be:

Options

A. `1.4.85times10^(-3)Omega`
B. `3times10^(-3)Omega`
C. `75times10^(-3)Omega`
D. `2.75times10^(-3)Omega`

Answer

To solve the problem, we need to find the value of the shunt resistance (S) required for a galvanometer to measure a maximum current of 8 A, given that the galvanometer shows full-scale deflection at a current of 3 mA and has a coil resistance of 8 Ω.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Coil resistance of the galvanometer (R_g) = 8 Ω
- Full-scale deflection current (I_g) = 3 mA = 3 × 10^(-3) A
- Maximum current to be measured (I) = 8 A

2. **Determine the Current through the Shunt:**
The current flowing through the shunt (I_s) can be calculated using the formula:
\[ I_s = I - I_g \]
Substituting the known values:
\[ I_s = 8 A - 3 × 10^{-3} A = 8 A - 0.003 A = 7.997 A \]

3. **Calculate the Voltage across the Galvanometer:**
The voltage across the galvanometer (V_g) when full-scale deflection occurs can be calculated using Ohm’s Law:
\[ V_g = I_g \times R_g \]
Substituting the values:
\[ V_g = (3 × 10^{-3} A) \times (8 Ω) = 24 × 10^{-3} V = 0.024 V \]

4. **Set Up the Equation for the Shunt:**
The voltage across the shunt (V_s) must be equal to the voltage across the galvanometer:
\[ V_s = I_s \times S \]
Since V_g = V_s, we can write:
\[ I_s \times S = V_g \]
Substituting the known values:
\[ 7.997 A \times S = 0.024 V \]

5. **Solve for the Shunt Resistance (S):**
Rearranging the equation to solve for S:
\[ S = \frac{V_g}{I_s} = \frac{0.024 V}{7.997 A} \]
Calculating S:
\[ S = 0.003 = 3 × 10^{-3} Ω = 3 mΩ \]

### Final Answer:
The value of the shunt resistance (S) required is **3 mΩ**.