The resistance RRR of a copper “gauge 10” jumper cable with diameter d=0.259d=0.259 cmcm is 0.0124 ΩΩ. Find the length LLL of the cable. Exp

Question

The resistance RRR of a copper “gauge 10” jumper cable with diameter d=0.259d=0.259 cmcm is 0.0124 ΩΩ. Find the length LLL of the cable. Express your answer in mm. Use three significant figures.

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Mít Mít 5 years 2021-08-20T12:38:01+00:00 1 Answers 70 views 1

Answers ( )

  1. quangkhai
    0
    2021-08-20T12:39:33+00:00
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    Answer:

    The length will be “3.89 m“.

    Explanation:

    The given values are:

    Diameter,

    d = 0.259 cm

    On converting it in m, we get

    d = 0.259 × 10⁻²            

    Resistance

    R = 0.0124 Ω      

    As we know,

    ⇒  A=\pi (\frac{d}{2})^2

    On putting the estimated values, we get

            =3.14(\frac{0.259\times 10^{-2}}{2})^2

            =5.266\times 10^{-6} \ m^2

    If, \rho = 1.68\times 10^{-8} \ \Omega.m

    then, R=\frac{\rho L}{A}

             L=\frac{RA}{\rho}

    On substituting the values, we get

                =\frac{(0.0124)(5.266\times 10^{-6})}{1.68\times 10^{-8}}

                =3.89 \ m

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