High–frequency signals are often transmitted along a coaxial cable, such as the

Question

High–frequency signals are often transmitted along a coaxial cable, such as the one shown on the right. For example, the cable TV hookup coming into your home is a coaxial cable. The signal is carried on a wire of radius R1 while the outer conductor of radius R2 is grounded (i.e., at V=0V). An insulating material fills the space between them, and an insulating plastic coating goes around the outside.

a. Find an expression for the capacitance per meter of a coaxial cable. Assume the insulating material between the cylinders is air.

b. What is the capacitance per meter if the insulating material (air) between is replaced with pure water?

c. Evaluate the capacitance per meter of a cable where R1=0.50mm and R2=3.0mm.

Explanation / Answer

a) Capacitance per unit length of cyllindrical capacitor when the gap is fileed with air,

C/L = 2*pi*epsilon/ln(R2/R1)

here

R2 is outer radius

R1 is ineer radius

b) when the gap is filled with water

C/L = 2*pi*k*epsilon/ln(R2/R1)

here, k is dielectric constant of the medium between the two plates.

c) we know, for water, k = 80.4

so,
C/L = 2*pi*80.4*8.854*10^-12/ln(3/0.5)

= 2.5*10^-9 F of 2.5 nF

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