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16 August, 03:45

A particular wire has a resistivity of 6.47*10-8 Ωm and a cross-sectional area of 2.32 mm2. A length of this wire is to be used as a resistor that will develop 130 W of power when connected to a 9.00 V battery. What length of wire is required?

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  1. 16 August, 04:03
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    Using the formula for power:

    P = V^2 / R

    130 W = (9.00 V) ^2 / R

    Solve for r:

    R = 81/130

    R = 0.623 ohms

    Now solve for the length of wire:

    R = rho L / A

    A must be in m^2 - 2.32 mm^2 * 1 m^2/10^6 mm^2 = 2.132x10^-6 m^2

    Now you have:

    0.623 = (6.47x10^-8) L / (2.32x10^-6)

    L = 22.34 m (Round answer as needed.)
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