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15 October, 10:33

A wire is hung between two towers and has a length of 208 m. A current of 154 A exists in the wire, and the potential difference between the ends of the wire is 0.245 V. The density of the wire material is 3610 kg/m3 and its resistivity is 4.23 x 10-8Ω·m. Find the mass of the wire.

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Answers (2)
  1. 15 October, 10:47
    0
    Mass = 4152kg

    Explanation:

    Given

    L = 208m

    I = 154A

    V = 0.245V

    Density = 3610 kg/m3

    ρ = 4.23 x 10-8Ω·m = resistivity of wire

    Resistance R = ρL / A

    R = voltage / current = V/I = 0.245/154 = 1.59*10-³ohms

    1.59*10-³ = 4.23 x 10-⁸*208/A

    Rearranging,

    A = 4.23 x 10-⁸*208/1.59*10-³

    A = 5.53*10-³m²

    Mass = density * volume

    Volume = L*A = 208*5.53*10-³m³ = 1.15m³

    Mass = 3610*1.15 = 4152kg
  2. 15 October, 10:59
    0
    Given Information:

    Length of wire = L = 208 m

    Current in wire = I = 154 A

    Voltage across wire = V = 0.245 V

    Resistivity of wire = ρ = 4.23x10⁻⁸ Ω. m

    Density of wire = d = 3610 kg/m³

    Required Information:

    Mass of wire = m = ?

    Answer:

    Mass of wire = 4152.36 kg

    Explanation:

    The mass of wire can be found using

    m = dAL

    where d is the density of wire, A is the area of wire and L is the length of wire.

    First we need to find area A, we know that resistivity of wire is given by

    ρ = RA/L

    A = ρL/R

    First we need to find R, we know know that resistance is given by

    R = V/I

    R = 0.245/154

    R = 0.00159 Ω

    So the area becomes,

    A = ρL/R

    A = (4.23x10⁻⁸*208) / 0.00159

    A = 0.00553 m²

    Finally, the mass of wire is

    m = dAL

    m = 3610*0.00553*208

    m = 4152.36 kg

    Therefore, the mass of wire is 4152.36 kg
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