A straight cylindrical wire having a length of 1.00m & a diameter of 0.40mm is made of a material that obeys..

...Ohm's law with a resistivity of p=8x10^-8 ohms m. If a potential of 8 Volts is maintained across the length of the wire (i.e. between the ends) find (a) the electric field in the wire, (b) the resistance of the wire, (c) the electric current in the wire, (d) the current density in the wire and (e) the drift speed if the number of conduction electrons is 17x10^22 per cubic centimeter. Any help would be greatly appreciated.. :)

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  • Anonymous
    1 decade ago
    Favorite Answer

    a)

    electric field (E) = 8V / 1m

    E = 8 V/m

    b)

    resistance (R)

    A(circle) = pi * r²

    A = 3.1416 * (0.20/1000)²

    A = 1.2566x10^-7

    R = pL / A

    R = (8x10^-8)(1) / 1.2566x10^-7

    R = 0.6366 ohm

    c)

    electric current (I)

    I = V/R

    I = 8 / 0.6366

    I = 12.566ampere

    d)

    current density (J)

    J= I/A

    J = 50.2655 / 1.2566x10^-7

    J = 100,000,000 Ampere/m²

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  • Sparks
    Lv 6
    1 decade ago

    (a).

    Electric field = voltage / length

    Electric field = 8 / 1

    Electric field = 8 V/m.

    (b).

    D = 0∙4mm

    → r = 0∙2 mm

    → r = (0∙2)/1000 m

    → r = 0∙0002 m

    A = π r²

    A = π(0∙0002)²

    A = 0∙000 000 125...

    A = 125*10^-9 m²

    R = pL / A

    R = (8*10^-8)(1) / (125*10^-9)

    R = 0∙6636 619 772...Ω

    R ≈ 0∙6636 Ω

    (c).

    I = V/R

    I = 8 / 0∙6636 619 772...

    I = 12∙566 370 61...

    I ≈ 12∙566 A

    (d).

    D = I / A

    D = 12∙566 370 61... / 125*10^-9

    D = 100 530 964∙9

    D ≈ 100 * 10^6 A/m²

    (e).

    Drift electrons per unit area will be the issue.

    1m² = 100cm * 100cm

    1m² = 10,000cm²

    But the area of the conductor is: 125*10^-9m²

    1m² * 125*10^-9 = 10,000 * 125*10^-9cm²

    125*10^-9m² = 1∙570 796 327 * 10^-14cm²

    But 17*10^22 electrons pass through a cm² surface area:

    No. of electrons = 1∙570 796 327 * 10^-14cm² * 17*10^22

    No. of electrons = 267 035 3756

    No. of electrons ≈ 2∙67 * 10^9 electrons.

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  • 1 decade ago

    (a) Electric field = voltage/length = 8 / 1 = 8 N/C.

    (b) Resistance

    = ρ( l / A) = 8 x 10^(-8) * (1 / (pi/4)*(0.4 x 10^(-3)^2)

    = 0.64 Ω.

    (c) Current = voltage / resistance = 8 / 0.64 = 12.5 A.

    (d) Current density

    = current / cross-sectional area

    = 12.5 / (pi/4)*(0.4 x 10^(-3)^2

    = 10^8 A/m^2.

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  • 1 decade ago

    try reading the book didnt you take notes in class im not helpin you cheat on your test sorry

    Source(s): google ohms law calculater i did
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  • 1 decade ago

    ?????????????/

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