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12 April, 20:09

The resistance, R (in ohms), Of a wire varies directly with the length, L (in cm) of the wire, and inversely with the cross-sectional area, A (in cm2). A 500 cm piece of wire with a radius of 0.2 cm has a resistance of 0.025 ohm. Find an equation that relates these variables.

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  1. 12 April, 20:24
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    R = 2π*10⁻⁶ L / A

    Step-by-step explanation:

    Resistance varies directly with length and inversely with area, so:

    R = kL/A

    A round wire has cross-sectional area of:

    A = πr²

    Substituting:

    R = kL / (πr²)

    Given that R = 0.025 Ω when L = 500 cm and r = 0.2 cm:

    0.025 = k (500) / (π (0.2²))

    k = 2π*10⁻⁶

    Therefore:

    R = 2π*10⁻⁶ L / A
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