If the outer conductor of a coaxial cable has radius 2.6 mm , what should be the radius of the inner conductor so that the inductance per un

Question

If the outer conductor of a coaxial cable has radius 2.6 mm , what should be the radius of the inner conductor so that the inductance per unit length does not exceed 50 nH per meter? Express your answer using two significant figures.

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Farah 4 years 2021-08-26T08:40:50+00:00 1 Answers 4 views 0

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  1. thuhuong
    0
    2021-08-26T08:42:31+00:00
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    Answer:

    Inner radius = 2 mm

    Explanation:

    In a coaxial cable, series inductance per unit length is given by the formula;

    L’ = (µ/(2π))•ln(R/r)

    Where R is outer radius and r is inner radius.

    We are given;

    L’ = 50 nH/m = 50 × 10^(-9) H/m

    R = 2.6mm = 2.6 × 10^(-3) m

    Meanwhile µ is magnetic constant and has a value of µ = µ_o = 4π × 10^(−7) H/m

    Plugging in the relevant values, we have;

    50 × 10^(-9) = (4π × 10^(−7))/(2π)) × ln(2.6 × 10^(-3)/r)

    Rearranging, we have;

    (50 × 10^(-9))/(2 × 10^(−7)) = ln((2.6 × 10^(-3))/r)

    0.25 = ln((2.6 × 10^(-3))/r)

    So,

    e^(0.25) = (2.6 × 10^(-3))/r)

    1.284 = (2.6 × 10^(-3))/r)

    Cross multiply to give;

    r = (2.6 × 10^(-3))/1.284)

    r = 0.002 m or 2 mm

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