Verified answer

The resistivity of a conductor is given by (see ref. 1):

(1) ρ = R * A / L,

where

R = resistance = 15.0Ω

A = the cross-sectional area of the conductor

L = the length of the conductor = 48m

ρ = resistivity for nichrome = 1.5*10^-6 Ω m . . . .(see ref. 2)

Solving for A:

(2) A = ρ * L / R

= (1.5*10^-6) * 48 / 15.0

= 0.100*10^-6 * 48

= 4.80*10^-6 m^2

Area of a circle is:

(3) A = π * r^2

= 3.14 * (d/2)^2 = 3.14 * d^2/4 =>>

(4) d = sqrt (4 * A / 3.14)

= sqrt (4 * (4.80*10^-6) / 3.14)

= 0.00247m

= 2.47mm <<===diameter of nichrome wire required

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