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 1 year 2021-09-05T16:08:25+00:00 1 Answers 27 views 0

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    2021-09-05T16:09:26+00:00

    Answer:

    [tex]16\Omega[/tex]

    Explanation:

    Initial length of wire=[tex]L_0[/tex]

    Initial radius of wire=[tex]r_0[/tex]

    Resistance of wire=1 ohm

    After stretching

    Radius of wire=r=[tex]0.25r_0[/tex]

    New resistance  of wire=R

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

    [tex]V=A_0L_0=AL[/tex]

    [tex]\frac{L_0}{L}=\frac{A}{A_0}[/tex]…(1)

    [tex]R=\rho\frac{l}{A}[/tex]

    Using the formula

    [tex]1=\frac{\rho L_0}{A_0}[/tex]

    [tex]R=\frac{\rho L}{A}[/tex]

    Using equation (1)

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

    Area , A=[tex]\pi r^2[/tex]

    Substitute the values

    [tex]\frac{1}{R}=(\frac{\pi (0.25r_0)^2}{\pi(r_0)^2})^2=0.0625[/tex]

    [tex]R=\frac{1}{0.0625}=16\Omega[/tex]

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