##### Transmission Line L and C Computation

In a single phase circuit the inductance per line is

$$L=2\times {10}^{-7}\mathrm{ln}\frac{D}{{r}^{\prime}}\mathrm{H/m}$$

D is the distance between the conductors

r is the radius of the conductor

r^{'} = r.e^{-1/4}

The total inductance due to both lines is 2L

In three phase circuit the inductance per line is

$$L=2\times {10}^{-7}\mathrm{ln}\frac{{D}_{m}}{{D}_{s}}\mathrm{H/m}$$

D_{m} is the Geometric Mean distance (GMD) between the Phases conductors

D_{s} is the Geometric Mean Radius (GMR) of the conductors

The equation is used to find inductance for double, triple or any three phase multicircuit arrangement

(The lines are assumed as transposed)

In a single phase circuit the capacitance between line and neutral is:

$$C=\frac{2\pi {\mathrm{\epsilon}}_{\mathrm{o}}}{\mathrm{ln}\left[D/r\right]}\mathrm{F/m}$$

D is the distance between the conductors

r is the radius of the conductor

(Remember that in case of capacitance calculation r' is not used)

ε_{o} is the permittivity of free space, ε_{o} = 8.85x10^{-12} F/m

The capacitance between the lines is C/2 (as the capacitances in series behaves similar to resistances in parallel)

In three phase circuit the capacitance per line is

$$C=\frac{2\pi {\mathrm{\epsilon}}_{\mathrm{o}}}{\mathrm{ln}\left[{D}_{m}/{D}_{\mathrm{s\text{'}}}\right]}\mathrm{F/m}$$

D_{m} is calculated the same way as for inductance.

D_{s'} is the Geometric Mean Radius, calculated by using r in place of r' as in case of inductance.