A copper wire has radius r = 0.0205 cm, is 2.95 m long, has resistivity ρ = 1.72 · 10−8 Ω m, and carries a c?

A copper wire has radius r = 0.0205 cm, is 2.95 m long, has resistivity

ρ = 1.72 · 10−8 Ω m,

and carries a current of 0.370 A. The wire has density of charge carriers of 8.50 · 1028 electrons/m3. (When entering units, use ohm for Ω.)

(b) What is the electric potential difference, ΔV, across the wire?

(c) What is the electric field, E, in the wire? (Enter the magnitude of the electric field.)

2 Answers

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  • u.n. o
    Lv 5
    9 years ago
    Favorite Answer

    (a) and (b) - same as UV.

    (c): j = sigma*E, j = current density and E = electric field, sigma - conductivity

    sigma = 1/resistivity = A/(L*resistivity), L = length

    But R = (resistivity)*L/A

    So sigma = L/AR

    j = i/A i = current

    So E = j/sigma = iR/L

    PS UV: You meant rho, not R in your answer.

  • Quark
    Lv 6
    9 years ago

    (a) Resistance of the wire :

    R = ρ * L/A

    = 1.72 x 10^-8 * 2.95/(π * (2.05 x 10^-4)^2)

    = 0.384 Ω

    (b) ΔV =I * R

    = 0.370 * 0.384 = 0.142 volts

    (c) J = I/A = σ * E

    --> E = I/A * σ --> σ = 1/R

    --> E = I * R/A

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