A piece of Nichrome wire has a radius of 6.5 104 m. It is used in a laboratory to make a heater that uses 4.00 102 W of power when connect

Question

A piece of Nichrome wire has a radius of 6.5 104 m. It is used in a laboratory to make a heater that uses 4.00 102 W of power when connected to a voltage source of 120 V. Ignoring the effect of temperature on resistance, estimate the necessary length of wire.

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Khang Minh 4 years 2021-09-01T23:40:44+00:00 1 Answers 87 views 0

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  1. Philomena
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    2021-09-01T23:41:52+00:00
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    Answer:

    L=4.8*10^{17}m

    Explanation:

    Given data

    Power P=4.00×10²W

    Radius r=6.5×10⁴m

    Voltage V=120V

    To find

    Length of wire L

    Solution

    We know that resistance of wire can be obtained from

    P=\frac{V_{2}}{R}\\ R=\frac{V_{2}}{P}

    We also know that R=pL/A solving the length noting that A=πr²

    and using p=100×10⁻⁸Ω.m we find that

    So

    L=\frac{RA}{p}\\ L=\frac{\frac{(V^{2})}{P}(\pi r^{2}) }{p} \\L=\frac{V^{2}(\pi r^{2})}{pP}\\ L=\frac{(120V)^{2}\pi (6.5*10^{4} m)^{2} }{100*10^{-8}(4.00*10^{2} W) }\\ L=4.8*10^{17}m

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