Calculation of Capacitance in a Two-Wire Conduction Line

Given:
- Length of the conduction line (L) = 0.75 km = 750 m
- Center-to-center distance between the conductors (d) = 0.2 m
- Diameter of each conductor (D) = 4 cm = 0.04 m

Step 1: Calculating the Radius of the Conductor
The radius (r) of the conductor can be calculated using the formula:
r = D/2 = 0.04 m / 2 = 0.02 m

Step 2: Calculating the Permittivity of Free Space
The permittivity of free space (ε₀) is a physical constant and is given by:
ε₀ = 8.854 x 10^(-12) F/m

Step 3: Calculating the Capacitance per Unit Length
The capacitance per unit length (C') of the two-wire conduction line can be calculated using the formula:
C' = (πε₀) / ln(d/r)

Using the given values, we can substitute them into the formula:
C' = (π x 8.854 x 10^(-12) F/m) / ln(0.2 m / 0.02 m)

Step 4: Calculating the Total Capacitance
The total capacitance (C) of the two-wire conduction line can be calculated by multiplying the capacitance per unit length (C') by the length of the line (L):
C = C' x L

Substituting the values, we get:
C = (C' x 750 m)

Step 5: Evaluating the Capacitance
Evaluate the expression for C to find the capacitance of the two-wire conduction line.

Final Answer:
The capacitance of the two-wire conduction line is equal to the evaluated value of C.

Explanation:
The capacitance of a two-wire conduction line can be calculated using the formula C' = (πε₀) / ln(d/r), where C' is the capacitance per unit length, ε₀ is the permittivity of free space, d is the center-to-center distance between the conductors, and r is the radius of the conductor. By substituting the given values into the formula, we can calculate C'. Multiplying C' by the length of the line gives us the total capacitance, C. Finally, evaluating the expression for C yields the capacitance of the two-wire conduction line.