A single-phase line consists of two long solid conductors, each having a radius of r metre separated by a distance of D metre. What will be capacitance between the conductor?

Concept:

The capacitance between the conductors of a 1-ϕ, 2- long solid conductors transmission line:

D = distance of separation between two long solid conductors

r = radius of each long solid conductor 

q_A, q_B  = Charge across A and B conductors

The standard result for the capacitance between the conductors

C_AB = q_A / V_AB 

= q_B / V_BA 

= π ϵ_r ϵ_∘ / ln(D / r)       .....( i )

Calculations:

ϵ∘ = 8.85 × 10^-12 

ϵ_r  = 1 (for air)

π = 3.14

ln (D / r) = 2.303 log (D / r)

From equation ( i )

CAB = (3.14 × 8.85 × 10-12 × 1) / (2.303 log (D / r)) F/m

CAB = \(\frac{{0.0121}}{{\log \left( {\frac{D}{r}} \right)}}\mu F/km\)