**Capacitance of a Two Wire Line:**

Consider a Capacitance of a 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 *q _{a}* and

*q*so that

_{b}*q*

_{a}= — q_{b}.

The potential difference V_{ab} can be written in terms of the contributions made by *q _{a}* and

*q*by use of Eq. (3.2) with associated assumptions (i.e.

_{b}**is large and ground is far away). Thus,**

*Dlr*

The line capacitance *C _{ab}* is then

The associated line charging current is

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

The assumptions inherent in the above derivation are:

- 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

*
*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.

- 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.