The resistance of a wire of lengt L0 and radius r0 is 1 ohm If the wire is stretched so thay its radius becomes 0.25r0. what is the new resi

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The resistance of a wire of lengt L0 and radius r0 is 1 ohm If the wire is stretched so thay its radius becomes 0.25r0. what is the new resistance of the wire

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Sigridomena 4 years 2021-09-05T16:08:25+00:00 1 Answers 33 views 0

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  1. Nick
    0
    2021-09-05T16:09:26+00:00
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    Answer:

    16\Omega

    Explanation:

    Initial length of wire=L_0

    Initial radius of wire=r_0

    Resistance of wire=1 ohm

    After stretching

    Radius of wire=r=0.25r_0

    New resistance  of wire=R

    When the wire drawn under tensile stress  then volume remains constant.

    V=A_0L_0=AL

    \frac{L_0}{L}=\frac{A}{A_0}…(1)

    R=\rho\frac{l}{A}

    Using the formula

    1=\frac{\rho L_0}{A_0}

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

    Using equation (1)

    \frac{1}{R}=\frac{L_0A}{LA_0}=\frac{A}{A_0}\times \frac{A}{A_0}=(\frac{A}{A_0})^2

    Area , A=\pi r^2

    Substitute the values

    \frac{1}{R}=(\frac{\pi (0.25r_0)^2}{\pi(r_0)^2})^2=0.0625

    R=\frac{1}{0.0625}=16\Omega

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