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 in the figure above.

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. An insulating materiel 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 that the insulating material between the cylinders is air.

b) Evaluate the capacitance per meter of a cable having R1 = 0.50mm and R2 = 3.0mm.

Explanation / Answer

Here ,

for the charge Q on the cable ,

a) expression for the capacitance per meter

change in potential = integration(E.dr)

change in potential = 2 * k *lamda* integration(1/r).dr

change in potential = 2 * k *lamda*ln(R2/R1)

as Q = lamda * L

V = 2 * k *lamda*ln(R2/R1)

V = 2 * k *Q/L*ln(R2/R1)

as Q = C * V

C/L = 1/(2 * k * ln(R2/R1))

the capacitance per meter is 1/(2 * k * ln(R2/R1))

b)

C/L = 1/(2 * k * ln(R2/R1))

putting values

C/L = 1/(2 * 9*10^9 * ln(3/.5))

C/L = 3.1 *10^-11 F/m

the capacitance per m is 3.1 *10^-11 F/m

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