What is the resistance of a tungsten wire with a cross section of S = 0.1 mm2 and a mass

What is the resistance of a tungsten wire with a cross section of S = 0.1 mm2 and a mass of m = 7.72 g? density of tungsten D = 19.3 g / cm3

Given:

m = 7.72 grams is the mass of the tungsten wire;

ro = 19.7 grams / cubic centimeter – tungsten density;

s = 0.1 square millimeter is the cross-sectional area of ​​the wire;

r = 0.055 Ohm * mm2 / m is the resistivity of tungsten.

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

Let’s find the volume occupied by the wire:

V = m / ro = 7.72 / 19.7 = 0.39 cubic centimeters = 390 cubic millimeters.

Then the length of the wire is:

l = V / s = 390 / 0.1 = 3900 millimeters = 3.9 meters.

Then the resistance of the conductor will be equal to:

R = r * l / s = 0.055 * 3.9 / 0.1 = 0.055 * 39 = 2.1 ohms (the result is rounded to one decimal place).

Answer: the resistance of the conductor is 2.1 ohms.