A `5-A` wire can withstand a maximum power of `1W` in circuit. The resistance of the fuse wire is

Options

A. `0.2 Omega`
B. `5 Omega`
C. `0.4 Omega`
D. `0.04 Omega`

Answer

To find the resistance of the fuse wire, we can use the relationship between power, current, and resistance. The formula we will use is:

\[ P = I^2 R \]

Where:
- \( P \) is the power (in watts),
- \( I \) is the current (in amperes),
- \( R \) is the resistance (in ohms).

### Step-by-step Solution:

1. **Identify the given values**:
- Current, \( I = 5 \, \text{A} \)
- Maximum power, \( P = 1 \, \text{W} \)

2. **Rearrange the power formula to solve for resistance**:
\[ R = \frac{P}{I^2} \]

3. **Substitute the values into the formula**:
\[ R = \frac{1 \, \text{W}}{(5 \, \text{A})^2} \]

4. **Calculate \( I^2 \)**:
\[ (5 \, \text{A})^2 = 25 \, \text{A}^2 \]

5. **Substitute \( I^2 \) back into the resistance formula**:
\[ R = \frac{1 \, \text{W}}{25 \, \text{A}^2} \]

6. **Perform the division**:
\[ R = 0.04 \, \Omega \]

### Final Answer:
The resistance of the fuse wire is \( 0.04 \, \Omega \).

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