A certain fuse “blows” if the current in it exceeds 1.0 A, at which instant the fuse melts with a current density of What is the diameter of

Question

A certain fuse “blows” if the current in it exceeds 1.0 A, at which instant the fuse melts with a current density of What is the diameter of the wire in the fuse?

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Trúc Chi 4 years 2021-08-15T22:18:48+00:00 1 Answers 118 views 0

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  1. Nho
    0
    2021-08-15T22:20:31+00:00
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    Answer:

    0.45 mm

    Explanation:

    The complete question is

    a certain fuse “blows” if the current in it exceeds 1.0 A, at which instant the fuse melts with a current density of 620 A/ cm^2. What is the diameter of the wire in the fuse?

    A) 0.45 mm

    B) 0.63 mm

    C.) 0.68 mm

    D) 0.91 mm

    Current in the fuse is 1.0 A

    Current density of the fuse when it melts is 620 A/cm^2

    Area of the wire in the fuse = I/ρ

    Where I is the current through the fuse

    ρ is the current density of the fuse

    Area = 1/620 = 1.613 x 10^-3 cm^2

    We know that 10000 cm^2 = 1 m^2, therefore,

    1.613 x 10^-3 cm^2 = 1.613 x 10^-7 m^2

    Recall that this area of this wire is gotten as

    A = \frac{\pi d^{2} }{4}

    where d is the diameter of the wire

    1.613 x 10^-7 = \frac{3.142* d^{2} }{4}

    6.448 x 10^-7 = 3.142 x d^{2}

    d^{2} =\sqrt{ 2.05*10^-7}

    d = 4.5 x 10^-4 m = 0.45 mm

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