Determine the resistance of an electric furnace heating element made of constantan

Determine the resistance of an electric furnace heating element made of constantan wire with a diameter of 0.80 mm and a length of 24.2 m.

Given:

d = 0.8 millimeters – constantan wire diameter;

l = 24.2 meters – length of constantan wire;

r = 0.5 Ohm * mm2 / m is the resistivity of constantan.

It is required to determine R (Ohm) – the total resistance of the constantan wire.

Find the cross-sectional area of the wire:

s = n * d2 / 4, where n = 3.14 is a geometric constant.

s = 3.14 * 0.82 / 4 = 3.14 * 0.64 / 4 = 2/4 = 0.5 mm2.

Then, to determine the resistance, you must use the following formula:

R = r * l / s = 0.5 * 24.2 / 0.5 = 24.2 ohms.

Answer: The total resistance of the heating element is 24.2 ohms.