Final answer:
The capacitance of a 3-ft length of 35B/U coaxial cable with the given specifications is approximately 55.34 pF. This calculation requires converting units to meters, applying the capacitance per unit length formula for a coaxial cable, and then multiplying by the cable's length.
Step-by-step explanation:
To determine the capacitance of a 3-ft length of 35B/U coaxial cable, which has an inner conductor diameter of 0.35 inches, a polyethylene dielectric with a relative permittivity of εr = 2.26, and an outer conductor with an inner diameter of 0.90 inches, we use the following formula for the capacitance per unit length of a coaxial cable:
C' = 2πε0εr / ln(ro/ri)
where ε0 is the vacuum permittivity (8.854 x 10-12 F/m), εr is the relative permittivity of the dielectric material, ro is the inner radius of the outer conductor, and ri is the radius of the inner conductor.
First, convert all measurements to meters:
- 3 ft = 0.9144 m
- 0.35 in = 0.00889 m
- 0.90 in = 0.02286 m
Next, calculate the capacitance per unit length (C') and then multiply by the length of the cable to obtain the total capacitance (C).
C' = 2π * 8.854 x 10-12 * 2.26 / ln(0.02286/0.00889) = 60.5 pF/m
C = C' * L = 60.5 pF/m * 0.9144 m = 55.34 pF