3 Shunt Admittance 3 Shunt Admittance 3.2 Capacitance of N Conductors

3.1 Linear Charge Density Along a Single Conductor

Assuming that a group of n conductors carrying linear charge densities q₁, q₂, …, q_n are located above the ground plane, the voltage of conductor i to ground is

V_{i}=\frac{q_{1}ln\left(\frac{D_{i1}}{d_{i1}}\right)+\cdots+q_{i}ln\left(% \frac{D_{ii}}{d_{i}}\right)+\cdots+q_{n}ln\left(\frac{D_{in}}{d_{in}}\right)}{% 2\pi\epsilon}

(31)

where

q_i is the charge of conductor i in coulombs/meter.

d_i is the radius of conductor i.

D_ii is the distance between conductor i and its image (i.e. 2h_i in Figure 1).

d_ij is the distance between conductor i and conductor j.

D_ij is the distance between conductor i and the image of conductor j as illustrated in Figure 1.

$\epsilon$ is the permittivity of the medium.

Note: The distances associated with each logarithmic ratio (e.g. d_i and D_ii or d_in and D_in) of Equation 31 must be expressed in the same units.