5.1 Resistance

Determine the resistance of a solid copper conductor at 100 MHz as shown in Figure 5.1. The conductivity of copper, ?, equals 5.8 10 ⁷ siemens/meter.

Figure 5.1: Resistance

Solution:

R _s = [( ?f ?) / ?] ^1/2

? = 4 ? 10 ^?7 henries/meter

? = 5.8 10 ^?7 siemens/meter

r = d / 2 = 0.5 cm

l = 25 cm

ohms

5.2 Inductance

Determine the inductance of a copper coaxial cable as shown in Figure 5.2. The permeability of copper, ?, equals 4 ? 10 ^?7 henries/meter.

Figure 5.2: Inductance

Solution:

b = outer radius = 1.2/2 = 0.6 cm

a = inner radius = 0.5/2 = 0.25 cm

l = 25 cm

? = 4 ? 10 ^?7 henries/meter

L = (2 10 ^?7)(0.875) (0.25)

L = 0.4375 10 ^?7 henries

5.3 Capacitance

Two pennies are held 0.1 cm apart as shown in Figure 5.3. Determine the resulting capacitance. The permittivity of free space, ? ₀, equals 8.854 10 ^?12 farads/meter.

Figure 5.3: Capacitance

Solution:

? ₀ = 8.854 10 ^?12 farads/meter

A = ?r ² = ?(1 10 ^?2) ²

A = ? 10 ^?4

C = ? ₀(