The coil of a moving coil galvanometer has an effective area of 4x`10^(-2)` `m^(2)`. It is suspended in a magnetic field of 5x`10^(-2)` Wb `m^(-2)`. If deflection in the galvanometer coil is 0.2 rad when a current of 5 mA is passed through it, then

Options

A. torsional constant is `5xx10^(-5)N-m" rad"^(-1)`
B. current sensitivity is `40 rad` `A^(-1)`
C. torsional constant is `3xx10^(-3)` `N-m` `" rad"^(-1)`
D. current sensitivity is `40 deg` `A^(-1)`

Answer

To solve the problem step-by-step, we will calculate the torsional constant and the current sensitivity of the galvanometer using the given parameters.

### Given Data:
- Effective area of the coil, \( A = 4 \times 10^{-2} \, m^2 \)
- Magnetic field strength, \( B = 5 \times 10^{-2} \, Wb/m^2 \)
- Deflection angle, \( \phi = 0.2 \, rad \)
- Current, \( I = 5 \, mA = 5 \times 10^{-3} \, A \)

### Step 1: Calculate the Torsional Constant
The formula for the torsional constant \( k \) of a moving coil galvanometer is given by:

\[ k = \frac{IAB}{\phi} \]

Substituting the values into the formula:

\[ k = \frac{(5 \times 10^{-3} \, A) \times (4 \times 10^{-2} \, m^2) \times (5 \times 10^{-2} \, Wb/m^2)}{0.2 \, rad} \]

Calculating the numerator:

\[ = 5 \times 10^{-3} \times 4 \times 10^{-2} \times 5 \times 10^{-2} \]

\[ = 5 \times 4 \times 5 \times 10^{-3} \times 10^{-2} \times 10^{-2} \]

\[ = 100 \times 10^{-7} = 1 \times 10^{-5} \]

Now, dividing by the deflection:

\[ k = \frac{1 \times 10^{-5}}{0.2} = 5 \times 10^{-5} \, N \cdot m/rad \]

### Step 2: Calculate the Current Sensitivity
Current sensitivity \( S \) is defined as the deflection per unit current:

\[ S = \frac{\phi}{I} \]

Substituting the values:

\[ S = \frac{0.2 \, rad}{5 \times 10^{-3} \, A} \]

Calculating:

\[ S = \frac{0.2}{5 \times 10^{-3}} = 40 \, rad/A \]

### Summary of Results
- Torsional constant \( k = 5 \times 10^{-5} \, N \cdot m/rad \)
- Current sensitivity \( S = 40 \, rad/A \)

### Conclusion
The correct options based on the calculations are:
1. Torsional constant \( k = 5 \times 10^{-5} \, N \cdot m/rad \) (Option 1 is correct)
2. Current sensitivity \( S = 40 \, rad/A \) (Option 2 is correct)