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29 December, 02:57

Compute the resistance of a hardened copper rod 2 meters long and 8 mm in diameter if resistivity of the material is 1.756 x 10^ (-8) ohm-meters?

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  1. 29 December, 03:32
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    The resistance of the copper rod = 4.39*10⁻¹⁵ Ohms.

    Explanation:

    Resistance: This is the opposition to current flow in a circuit.

    The S. I unit of resistance is Ohms.

    R = Aσ/L ... Equation 1

    Where σ = resistivity of the copper, R = resistance of the copper rod, A = cross sectional area of the copper, L = length of the copper rod.

    Given:

    σ = 1.756*10⁻⁸ ohm-meters, L = 2 meters.

    But A = πd²/4

    Where d = 8 mm = (8/1000) m = 0.0008 m, π = constant = 3.143

    Therefore,

    A = 3.143 (0.0008) ²/4

    A = 0.0000005 m²

    Substituting these values into equation 1,

    R = 5*10⁻⁷*1.756*10⁻⁸/2

    R = (8.78 * 10⁻¹⁵) / 2

    R = 4.39*10⁻¹⁵ Ohms.

    Thus the resistance of the copper rod = 4.39*10⁻¹⁵ Ohms.
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