A transmission line has a span length of 300 metres, and the conductor weight is 1 .2 N/m. If the tension in the conductor is 6000 N, what is the sag? 

Explanation:

Transmission Line Sag Calculation:

Definition: Sag in a transmission line refers to the vertical distance between the highest point of the conductor (at the support) and the lowest point of the conductor (mid-span). Proper sag calculation is essential to ensure the mechanical stability and safe operation of the transmission line.

Given Data:

• Span length (L) = 300 metres
• Conductor weight (w) = 1.2 N/m
• Tension in the conductor (T) = 6000 N

Formula for Sag Calculation:

The sag for a transmission line conductor can be calculated using the following formula:

Sag (S) = (w × L²) / (8 × T)

Where:

• w = weight of the conductor per unit length
• L = span length of the conductor
• T = tension in the conductor
• S = sag

Step-by-Step Solution:

Substitute the given values into the formula:

S = (1.2 × 300²) / (8 × 6000)

First, calculate the numerator:

Numerator = 1.2 × 300² = 1.2 × 90000 = 108000

Next, calculate the denominator:

Denominator = 8 × 6000 = 48000

Now, divide the numerator by the denominator:

Sag (S) = 108000 / 48000 = 2.25 metres

Final Answer:

The sag of the transmission line conductor is 2.25 metres.

Correct Option Analysis:

The correct answer is Option 2, which states that the sag is 2.25 metres. This calculation is accurate based on the formula and the given values.

Additional Information

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

Option 1: 6 metres

This option is incorrect. If we calculate the sag using the formula provided, the result is 2.25 metres, not 6 metres. The value of 6 metres might be applicable for a different set of parameters, but it does not correspond to the given data.

Option 3: 5 metres

This option is also incorrect. Using the formula and the given data, the sag is calculated as 2.25 metres. The value of 5 metres is significantly higher and does not match the calculation.

Option 4: 1 metre

This option is incorrect. The sag of 1 metre is too low compared to the calculated value of 2.25 metres. This discrepancy indicates that the tension in the conductor and the weight of the conductor have not been correctly accounted for if this value were to be chosen.

Conclusion:

Understanding the sag calculation is crucial for designing and maintaining transmission lines. The correct sag ensures that the conductor remains mechanically stable and operates safely under various conditions. The calculated sag value of 2.25 metres is accurate and matches the given data, making Option 2 the correct choice. Proper sag calculation also helps prevent excessive stress on the conductor and minimizes the risk of contact with ground or nearby objects due to sagging.