Capacitance of Two Wire Line:

Consider a Capacitance of Two Wire Line shown in Fig. 3.3 excited from a single-phase source. The line develops equal and opposite sinusoidal charges on the two conductors which can be represented as phasors qa and qb so that qa = — qb.

Capacitance of Two Wire Line

The potential difference Vab can be written in terms of the contributions made by qa and qb by use of Eq. (3.2) with associated assumptions (i.e. D/r is large and ground is far away). Thus,

The line capacitance Cab is then

The associated line charging current is

Capacitance of Two Wire Line

As shown in Figs. 3.4 (a) and (b) the line-to-line capacitance can be equivalently considered as two equal capacitances is series. The voltage across the lines divides equally between the capacitances such that the neutral point n is at the ground potential. The capacitance of each line to neutral is then given by

Capacitance of Two Wire Line

The assumptions inherent in the above derivation are:

1. The charge on the surface of each conductor is assumed to be uniformly distributed, but this is strictly not correct.

If non-uniformity of charge distribution is taken into account, then

Capacitance of Two Wire Line
If D/2r » 1, the above expression reduces to that of Eq. (3.6)and the error caused by the assumption of uniform charge distribution is negligible.

2. The cross-section of both the conductors is assumed to be circular, while in actual practice stranded conductors are used. The use of the radius of the circumscribing circle for a stranded conductor causes insignificant error.