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16 March, 19:43

Consider two copper wires with the same cross-sectional area. Wire a is twice as long as wire b. How do the resistivities and resistances of the two wires compare?

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  1. 16 March, 20:00
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    from the equation 1 below, the ratio of the resistivity of wire b to its resistance is twice the ratio of the resistivity if wire A to its resistance.

    Explanation:

    R = (ρL) / A

    A = (ρL) / R

    Where A is cross sectional area,

    ρ is the resistivity

    L is length of wire

    R is resistance of wire.

    from the question the two wires have same cross sectional area.

    Aa = Ab; hence

    (ρaLa) / Ra = (ρbLb) / Rb

    La = 2Lb

    (ρa*2Lb) / Ra = (ρbLb) / Rb

    (2ρa) / Ra = (ρb) / Rb

    ρb/Rb = 2 * ρa/Ra ... equ 1
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