What is the fusing factor if the fuse constant is 20; the diameter of the round wire is 0.5 mm and the current rating of the fusing element is 5 A?

Explanation:

Fusing Factor Calculation

Definition: The fusing factor is the ratio of the minimum fusing current to the current rating of the fuse element. It indicates how much current the fuse can carry before it melts and breaks the circuit.

Given Data:

• Fuse constant (K) = 20
• Diameter of the round wire (d) = 0.5 mm
• Current rating of the fusing element (I) = 5 A

Formula: The fusing factor (F) can be calculated using the formula:

\(I_f = K \times d^{3/2}\)

Where,

• \(I_f\) = Minimum fusing current
• K = Fuse constant
• d = Diameter of the wire

First, we need to calculate the minimum fusing current \(I_f\).

\(I_f = 20 \times (0.5)^{3/2}\)

\(I_f = 20 \times (0.5)^{1.5}\)

\(I_f = 20 \times \sqrt{0.5}\)

Calculation:

\(\sqrt{0.5} \approx 0.7071\)

\(I_f = 20 \times 0.7071\)

\(I_f = 14.142\)

Now, the fusing factor (F) is given by:

\(F = \frac{I_f}{I}\)

\(F = \frac{14.142}{5}\)

\(F \approx 2.828\)

The correct option is:

Option 2: \(4 \times \sqrt{\frac{1}{2}}\)

This matches the calculated result, where the factor \(4 \times \sqrt{\frac{1}{2}}\) simplifies to approximately 2.828.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: \(4 \times \left(\frac{1}{2}\right)\)

This option is incorrect because it simplifies to 2, which is not the correct fusing factor for the given data.

Option 3: \(\frac{4}{3}\)

This option is also incorrect because it does not match the calculated fusing factor of approximately 2.828.

Option 4: 0

This option is incorrect as a fusing factor cannot be zero. A fusing factor of zero would imply that the fuse never melts, which is not possible.

Conclusion:

Understanding the calculation of the fusing factor is essential for ensuring the proper functioning of electrical circuits and protecting them from overcurrent conditions. The fusing factor helps in determining the appropriate fuse for a given application, ensuring safety and reliability in electrical systems.