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30 March, 13:30

A potential difference of 3.27 nV is set up across a 2.16 cm length of copper wire that has a radius of 2.33 mm. How much charge drifts through a cross section in 3.23 ms? Assume that the resistivity of copper is 1.69 * 10-8 Ω·m.

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  1. 30 March, 16:28
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    Charge = 4.9096 x 10⁻⁷ C

    Explanation:

    First, we find the resistance of the copper wire.

    R = ρL/A

    where,

    R = resistance = ?

    ρ = resistivity of copper = 1.69 x 10⁻⁸ Ω. m

    L = Length of wire = 2.16 cm = 0.0216 m

    A = Cross-sectional area of wire = πr² = π (0.00233 m) ² = 1.7 x 10⁻⁵ m²

    Therefore,

    R = (1.69 x 10⁻⁸ Ω. m) (0.0216 m) / (1.7 x 10⁻⁵ m²)

    R = 2.14 x 10⁻⁵ Ω

    Now, we find the current from Ohm's Law:

    V = IR

    I = V/R

    I = 3.27 x 10⁻⁹ V/2.14 x 10⁻⁵ Ω

    I = 1.52 x 10⁻⁴ A

    Now, for the charge:

    I = Charge/Time

    Charge = (I) (Time)

    Charge = (1.52 x 10⁻⁴ A) (3.23 x 10⁻³ s)

    Charge = 4.9096 x 10⁻⁷ C
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