A three phase 50 Hz transmission line has flat horizontal spacing with 3.5 m between adjacent conductors. The conductors are No. 2/0 hard drawn copper (outside diameter = 1.05cm). The voltage f the line is 110 kV. The capacitance to neutral per kilometre of line is

To calculate the capacitance to neutral per kilometer of a three-phase transmission line, we can use the formula for the capacitance per unit length for a three-phase line with flat horizontal spacing.

The capacitance to neutral (C) can be calculated using the following formula:

[

C = frac{2 pi varepsilon_0}{ln(frac{D}{r})}

]

Where:

– ( varepsilon_0 ) is the permittivity of free space, approximately ( 8.854 times 10^{-12} , text{F/m} ).

– ( D ) is the distance between the conductors.

– ( r ) is the radius of the conductor.

1. The distance ( D ) between the conductors is given as 3.5 m.
2. The radius ( r ) of each conductor can be calculated from the outside diameter:

– Outside diameter = 1.05 cm = 0.0105 m, so the radius ( r = frac{0.0105}{2} = 0.00525 , text{m} ).

Now substituting these values into the formula:

1. Calculate ( ln(frac{D}{r}) ):

[

D = 3.5 , text{m} quad text{and} quad r = 0.00525 , text