# 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.