An eighteen gauge copper wire has a nominal diameter of 1.02mm. This wire carries a constant current of 1.67A to a 200w lamp. The density of

Question

An eighteen gauge copper wire has a nominal diameter of 1.02mm. This wire carries a constant current of 1.67A to a 200w lamp. The density of free electrons is 8.5 x 1028 electrons per cubic metre. Find the magnitude of:
i. The current density ii. The drift velocity

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niczorrrr 6 months 2021-07-18T05:15:13+00:00 1 Answers 61 views 0

Answers ( )

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    2021-07-18T05:17:08+00:00

    Answer:

    The current density is  J = 2.04 * 10^{6}  A /m^2

    The drift velocity is  v_d = 1.5 * 10^{-4} m/s

    Explanation:

    From the question we are told that

      The nominal diameter of the wire is d = 1.02 mm= \frac{1.02}{1000}  = 0.00102 \ m

       The current carried by the wire is I = 1.67 A

        The power rating of the lamp is P = 200 W

        The density of electron is n =  8.5 * 10^{28} \ e/m^3

       

    The current density is mathematically represented as

           J = \frac{I}{A}

    Where A is the area which is mathematically evaluated as

              A = \pi \frac{d^2}{4}

    Substituting values

             A = 3.142 * \frac{(1.02  *  10^{-3})^2 }{4}

           A = 8.0*10^{-4}m^2

    So

             J = \frac{1.67}{8.0*10^{-4}}

           J = 2.04 * 10^{6}  A /m^2

    The drift velocity is mathematically represented as

           v_d  = \frac{J}{ne}

    Where e is the charge on one electron which has a value  e = 1.602 *10^{-19} C

    So

             v_d =\frac{2.04 * 10^6 }{8.5 *10^{28} * 1.6 * 10^{-19}}

            v_d = 1.5 * 10^{-4} m/s

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