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4 October, 14:10

Calculate the current through a 15.0-m long 20 gauge (having radius 0.405 mm) nichrome wire if it is connected to a 12.0-V battery. The resistivity of nichrome is 100 * 10-8 Ω ∙ m.

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  1. 4 October, 17:00
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    Given Information:

    Radius of wire = r = 0.405 mm = 0.405*10⁻³ m

    Length of wire = L = 15 m

    Voltage = V = 12 V

    Resistivity = ρ = 100*10⁻⁸ Ωm

    Required Information:

    Current = I = ?

    Answer:

    Current = I = 0.412 A

    Explanation:

    The current flowing through the wire can be found using Ohm's law that is

    V = IR

    I = V/R

    Where V is the voltage across the wire and R is the resistance of the wire.

    The resistance of the wire is given by

    R = ρL/A

    Where ρ is the resistivity of the wire, L is the length of the wire and A is the area of the cross-section and is given by

    A = πr²

    A = π (0.405*10⁻³) ²

    A = 0.515*10⁻⁶ m²

    So the resistivity of the wire is

    R = ρL/A

    R = (100*10⁻⁸*15) / 0.515*10⁻⁶

    R = 29.126 Ω

    Finally, the current flowing through the wire is

    I = V/R

    I = 12/29.126

    I = 0.412 A

    Therefore, the current through a 15.0-m long 20 gauge nichrome wire is 0.412 A.
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