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 given that a 5-A wire can withstand a maximum power of 1 W, we can use the formula for electrical power.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Current (I) = 5 A
- Power (P) = 1 W

2. **Use the Power Formula:**
The power in an electrical circuit can be expressed using the formula:
\[ P = I^2 R \]
where:
- \( P \) is the power in watts,
- \( I \) is the current in amperes,
- \( R \) is the resistance in ohms.

3. **Rearrange the Formula to Solve for Resistance (R):**
To find the resistance, we can rearrange the formula:
\[ R = \frac{P}{I^2} \]

4. **Substitute the Given Values:**
Now, substitute the values of power and current into the formula:
\[ R = \frac{1 \, \text{W}}{(5 \, \text{A})^2} \]

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

6. **Calculate Resistance (R):**
Now substitute this back into the equation for resistance:
\[ R = \frac{1 \, \text{W}}{25 \, \text{A}^2} = 0.04 \, \Omega \]

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

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