# Q1:a) Discuss the effect of earth on the capacitance of a line :b) Derive in expression for the capacitance to neutral per phase per Km of a single phase overhead transmission line, taking into account the effect of earth.c) Derive in expression for the capacitance to neutral per phase per Km of a 3- phase overhead transmission line when conductors are of equilateral spacing.

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Q1:

a) Discuss the effect of earth on the capacitance of a line :

b) Derive in expression for the capacitance to neutral per phase per Km of a single phase overhead transmission line, taking into account the effect of earth.

c) Derive in expression for the capacitance to neutral per phase per Km of a 3- phase overhead transmission line when conductors are of equilateral spacing.

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Step 1

(a) The earth can be considered as a conducting infinite equipotential plane. The electric flux lines of the conductors are forced to cut the surface of the earth orthogonally. And the positive charge on the conductor will induce negative charge on the earth surface. To show this effect, we can assume the presence of an imaginary conductor of opposite charge of the actual conductor, below the surface of the earth at a depth equal to the height of the actual conductor above the surface of the earth. Thus, for the calculation of capacitance, the earth can be replaced by a fictitious charged conductor and this imaginary conductor is called the image of the actual conductor.

Step 2

(b) Let us say that the conductors a and b constitute the transmission line and the conductors a′ and b′ their corresponding images as shown below. The derivation of the expression for the capacitance to neutral per phase per Km of a single-phase overhead transmission line, considering the effect of earth is shown below:

Step 3

(c) The derivation is...

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### Electrical Engineering 