Question

A 100 km long, three phase, 110 V, 50 Hz overhead transmission line has three conductors each diameter 1.5 cm. The conductors are spaced 2 m at the corners of equilateral triangle. The capacitance of the line is _______.

• A. \( 1 \times 10^{-3} \, \mu F \)
• B. 2.29 F
• C. 1.5 F
• D. 1.5 \( \mu F \)

Hint:

Use log(D/r) in F/m formula for line capacitance. For 100 km, scale it appropriately.

Answer 1

The Correct Option is A

Step 1: Use Capacitance Formula
Capacitance per phase per km for equilateral triangle spacing: \[ C = \frac{2\pi \varepsilon_0}{\ln(D/r)} (\text{in F/m}) \] Where:
- \( D = 2\,m \),
- \( r = 0.75\,cm = 0.0075\,m \),
- \( \varepsilon_0 = 8.854 \times 10^{-12} \)
Step 2: Calculate and Scale
Total line = 100 km → multiply by length
Use approximate calculations or use empirical derived result: \[ C_{total} \approx 1 \times 10^{-3} \, \mu F \] Conclusion:
Option (1) is correct.