A heater is being designed that uses a coil of 14-gauge nichrome wire to generate 300 W using a voltage of V = 110 V . How long should the e

Question

A heater is being designed that uses a coil of 14-gauge nichrome wire to generate 300 W using a voltage of V = 110 V . How long should the engineer make the wire?(Note 14-guage wire has a diameter of 1.63 mm.)

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Phúc Điền 3 years 2021-08-22T17:39:04+00:00 1 Answers 62 views 0

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    2021-08-22T17:40:39+00:00

    Answer:

    The length of the wire is 83.2 m.

    Explanation:

    Given that,

    Power of heater, P = 300 W

    Voltage, V = 110 V

    The resistivity of nichrome wire is, \rho=100\times 10^{-8}\ \Omega-m

    The electric power of a wire is given by :

    P=\dfrac{V^2}{R}\\\\R=\dfrac{V^2}{P}\\\\R=\dfrac{(110)^2}{300}\\\\R=40.34\ \Omega

    Area of cross section of the wire is :

    A=\pi r^2\\\\A=\pi (0.000815)^2\\\\A=2.08\times 10^{-6}\ m^2

    Resistance of a material is given by :

    R=\rho \dfrac{L}{A}\\\\L=\dfrac{RA}{\rho}\\\\L=\dfrac{40\times 2.08\times 10^{-6}}{10^{-6}}\\\\L=83.2\ m

    So, the length of the wire is 83.2 m. Hence, this is the required solution.

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