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    The potential difference across a conductor of resistivity ρ is kept constant. The heat generated in the conductor is directly proportional to:
    Question

    The potential difference across a conductor of resistivity ρ is kept constant. The heat generated in the conductor is directly proportional to:

    A.

    ρ

    B.

    1 / √ρ

    C.

    1 / ρ

    D.

    ρ²

    Correct option is C


    Correct Answer: C — 1 / ρ
    Explanation
    According to Joule’s law of heating, the heat produced in a conductor is given by:
    Heat generated, H = V² t / R
    where:
    · V = potential difference (constant)
    · t = time (constant)
    · R = resistance
    So, H ∝ 1 / R
    Now, resistance R of a conductor is related to resistivity ρ by:
    R = ρ L / A
    where:
    · L = length of conductor
    · A = cross-sectional area
    For a given conductor, L and A are constants, so:
    R ∝ ρ
    Therefore,
    H ∝ 1 / ρ

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