To solve the problem of finding the shunt resistance required to convert a galvanometer into an ammeter with a specific range, we can follow these steps:
### Step-by-Step Solution:
1. **Identify Given Values**:
- Current through the galvanometer, \( I_G = 0.002 \, \text{A} \)
- Resistance of the galvanometer, \( R_G = 50 \, \Omega \)
- Desired range of the ammeter, \( I = 0.5 \, \text{A} \)
2. **Understand the Concept of Shunt Resistance**:
- To convert a galvanometer into an ammeter, a shunt resistance \( R_S \) is connected in parallel with the galvanometer. The shunt allows most of the current to bypass the galvanometer, while a small portion still passes through it.
3. **Use the Formula for Shunt Resistance**:
- The formula for shunt resistance \( R_S \) is given by:
\[
R_S = \frac{I_G \cdot R_G}{I - I_G}
\]
- Where:
- \( I_G \) is the current through the galvanometer,
- \( R_G \) is the resistance of the galvanometer,
- \( I \) is the total current passing through the ammeter.
4. **Substitute Given Values into the Formula**:
- Substitute \( I_G = 0.002 \, \text{A} \), \( R_G = 50 \, \Omega \), and \( I = 0.5 \, \text{A} \):
\[
R_S = \frac{0.002 \cdot 50}{0.5 - 0.002}
\]
5. **Calculate the Denominator**:
- Calculate \( 0.5 - 0.002 = 0.498 \).
6. **Calculate the Numerator**:
- Calculate \( 0.002 \cdot 50 = 0.1 \).
7. **Final Calculation**:
- Now substitute back into the formula:
\[
R_S = \frac{0.1}{0.498} \approx 0.2004 \, \Omega
\]
- Rounding to two decimal places, we find:
\[
R_S \approx 0.2 \, \Omega
\]
8. **Conclusion**:
- The required shunt resistance to convert the galvanometer into an ammeter of range 0.5 A is \( R_S = 0.2 \, \Omega \).
