6.1 Line resistance

A solid round wire conductor, made of annealed copper, has a length of five kilometers as shown in Figure 6.1. The wire diameter is 0.25 cm and its resistivity constant, ?, equals 1.7241 10 ^?8, meter-ohms at 20 C. Determine the conductor dc resistance at 20 C and 40 C using a zero resistance temperature of ?234.5 C.

Figure 6.1: Line resistance

Solution:

? = 1.7241 10 ^?8 meter-ohms at 20 C

R = 17.56 ohms at 20 C

R ₁ = 18.94 ohms at 40 C

6.2 Line inductance

A two conductor solid copper wire transmisson line extends for five kilometers. Each wire diameter is 0.25 cm and are spaced at a uniform distance of 30 cm apart as shown in Figure 6.2. Determine the line inductance, L _T.

Figure 6.2: Line inductance

Solution:

? = ? _r ? ₀

? _r = 1, ? ₀ = 4 ? 10 ^?7

L ₁ = L _int + L _ext = [(4 ? 10 ^?7)/(8 ?)] + [(4 ? 10 ^?7)/(2 ?)]In(D/r ₁)

L ₁ = 2 10 ^?7[(1/4) + In(D/r ₁)] henries/meter

L = L ₁ + L ₂

Due to symmetry L ₁ = L ₂

L = 2L ₁ = 4 10 ^?7In[(1.284D)/r ₁)]

L _T