If `2%` of the main current is to be passed through the galvanometer of resistance `G`, the resistance of shunt required is

Options

A. `G/49`
B. `G/50`
C. `49 G`
D. `50G`

Explanation

To solve the problem of finding the resistance of the shunt required when 2% of the main current is to be passed through a galvanometer of resistance \( G \), we can follow these steps:

### Step-by-Step Solution:

1. **Define the Variables**:
- Let the main current be \( I \).
- The current through the galvanometer is \( \frac{2}{100} I = 0.02 I \).
- The current through the shunt (the remaining current) is \( I - 0.02 I = 0.98 I \).

2. **Understand the Circuit Configuration**:
- The galvanometer and the shunt are connected in parallel. Therefore, the potential difference across both the galvanometer and the shunt is the same.

3. **Apply Ohm's Law**:
- The potential difference across the galvanometer can be expressed as:
\[ V = I_g \cdot G = (0.02 I) \cdot G \]
- The potential difference across the shunt can be expressed as:
\[ V = I_s \cdot R_s = (0.98 I) \cdot R_s \]
- Here, \( R_s \) is the resistance of the shunt.

4. **Set the Two Expressions for Voltage Equal**:
- Since the potential differences are the same, we can set the two equations equal to each other:
\[ (0.02 I) \cdot G = (0.98 I) \cdot R_s \]

5. **Cancel Out the Current \( I \)**:
- Since \( I \) is common in both terms and is not zero, we can cancel it out:
\[ 0.02 G = 0.98 R_s \]

6. **Solve for the Shunt Resistance \( R_s \)**:
- Rearranging the equation gives:
\[ R_s = \frac{0.02 G}{0.98} \]
- Simplifying this further:
\[ R_s = \frac{2}{98} G = \frac{G}{49} \]

### Conclusion:
The resistance of the shunt required is:
\[ R_s = \frac{G}{49} \, \text{Ohm} \]