# How long should a nichrome conductor with a diameter of 1.2 mm be taken for an electric furnace

How long should a nichrome conductor with a diameter of 1.2 mm be taken for an electric furnace so that when it is connected to a 220V network, the current is 5A?

1. Let’s translate given in the SI system:
d = 1.2 m = 1.2 * 10-3 m2
2. 2. Let’s write down the expression to determine the resistivity of the conductor:
ρsp = R * Ssech / l, where R is the resistance of the conductor, l is the length of the conductor, Ssech is the cross-sectional area.
3. Let us express l from here:
l = R * Ssec / ρsp
ρsp of nichrome will be determined according to the reference book 1.1 * 10-6 Ohm * m
4.Cross sectional area of ​​wire:
Ssection = π * d² / 4
5. Let’s put the expression from point 4 into the expression from point 3:
l = R * π * d² / (4 * ρsp)
6. According to Ohm’s law:
I = U / R
Let us express the resistance from this expression and substitute it into the formula 5
R = U / I
l = U * π * d² / (I * 4 * ρsp)
7. Substituting the numerical values, we have:
l = U * π * d² / (I * 4 * ρsp) = 220 * 3.14 * (1.2 * 10-3) ² / (5 * 4 * 1.1 * 10-6) = 45.2 m

Answer: 45.2 m of nichrome conductor is required.

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