A moving coil galvanometer has 50 turns and each turn has an area 210 . The magnetic field produced by the magnet inside the galvanometer is 0.02 . The torsional constant of the suspension wire is 10 . When a current flows through the galvanometer, a full scale deflection occurs if the coil rotates by 0.2 . The resistance of the coil of the galvanometer is 50 . This galvanometer is to be converted into an ammeter capable of measuring current in the range 01.0 . For this purpose, a shunt resistance is to be added in parallel to the galvanometer. The value of this shunt resistance, in , is __________.

Explanation

To solve the problem of finding the shunt resistance required to convert the moving coil galvanometer into an ammeter, we can follow these steps:

### Step 1: Identify Given Values
We have the following values from the problem:
- Number of turns (n) = 50
- Area of each turn (A) = 210 m² (Note: This seems incorrect; it should be 2 x 10^-4 m²)
- Magnetic field (B) = 0.02 T
- Torsional constant (k) = 10^-4 N·m/rad
- Full-scale deflection angle (θ) = 0.2 rad
- Resistance of the galvanometer (R_g) = 50 Ω
- Maximum current for ammeter (I) = 1.0 A

### Step 2: Calculate the Current through the Galvanometer (I_g)
Using the formula for the torque on the coil in the galvanometer:
\[ B \cdot I_g \cdot A \cdot n = k \cdot \theta \]
Substituting the known values:
\[ 0.02 \cdot I_g \cdot (2 \times 10^{-4}) \cdot 50 = 10^{-4} \cdot 0.2 \]
Calculating the left side:
\[ 0.02 \cdot I_g \cdot 10^{-2} = 10^{-4} \cdot 0.2 \]
\[ 0.0002 \cdot I_g = 0.00002 \]
Now, solving for \(I_g\):
\[ I_g = \frac{0.00002}{0.0002} = 0.1 \text{ A} \]

### Step 3: Set Up the Equation for Shunt Resistance (R_s)
The galvanometer is to be converted into an ammeter, so we need to find the shunt resistance \(R_s\). The current through the galvanometer is \(I_g\) and the total current is \(I\). The relationship can be expressed as:
\[ I_g \cdot R_g = (I - I_g) \cdot R_s \]
Substituting the known values:
\[ 0.1 \cdot 50 = (1 - 0.1) \cdot R_s \]
\[ 5 = 0.9 \cdot R_s \]

### Step 4: Solve for Shunt Resistance (R_s)
Now, we can solve for \(R_s\):
\[ R_s = \frac{5}{0.9} \approx 5.56 \, \Omega \]

### Final Answer
The value of the shunt resistance \(R_s\) required is approximately **5.56 Ω**.

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