A DC ammeter has resistance `0.1 Omega` and its current ranges `0-100 A`. If the range is to be extended to `0-500`, then the following shunt resistance will be required

Options

A. `0.010 Omega`
B. `0.011 Omega`
C. `0.025 Omega`
D. `0.25 Omega`

Answer

To solve the problem of extending the current range of a DC ammeter from 0-100 A to 0-500 A using a shunt resistor, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Current Distribution**:
- The ammeter can measure a maximum of 100 A. To extend its range to 500 A, we need to allow 400 A to bypass the ammeter through a shunt resistor (R_sh).
- Therefore, when 500 A flows through the circuit, 100 A will go through the ammeter, and 400 A will go through the shunt resistor.

2. **Use the Current Division Rule**:
- According to the current division rule in parallel circuits, the current through each resistor is inversely proportional to its resistance.
- Let I_a = 100 A (current through the ammeter) and I_sh = 400 A (current through the shunt resistor).
- The relationship can be expressed as:
\[ \frac{I_a}{I_sh} = \frac{R_sh}{R_a} \]
- Here, R_a is the internal resistance of the ammeter (0.1 Ω).

3. **Substitute Known Values**:
- Substitute the known values into the equation:
\[ \frac{100}{400} = \frac{R_sh}{0.1} \]

4. **Simplify the Equation**:
- Simplifying the left side gives:
\[ \frac{1}{4} = \frac{R_sh}{0.1} \]

5. **Solve for R_sh**:
- Cross-multiply to solve for R_sh:
\[ R_sh = 0.1 \times \frac{1}{4} = 0.1 \times 0.25 = 0.025 \, \Omega \]

6. **Conclusion**:
- The required shunt resistance (R_sh) to extend the ammeter's range to 0-500 A is 0.025 Ω.

### Final Answer:
The shunt resistance required is **0.025 Ω**.