What is the resistance of a platinum filament with a cross-sectional radius of 0.2 mm and a length of 6 cm?

Given:

n = 0.2 mm (millimeter) is the cross-sectional radius of the platinum filament;

l = 6 centimeters = 0.06 meters – thread length;

r = 0.107 Ohm * mm2 / m – specific section of platinum.

It is required to determine R (Ohm) – the resistance of the platinum filament.

Find the cross-sectional area of the platinum filament:

s = 2 * n * n, where n = 3.14 is the Pythagorean number.

s = 2 * 3.14 * 0.2 = 6.28 * 0.2 = 1.256 mm2 (square millimeters).

Then the resistance of the thread will be equal to:

R = r * l / s = 0.107 * 0.06 / 1.256 = 0.00642 / 1.256 = 0.005 Ohm (the result has been rounded to one thousandth).

Answer: the resistance of the platinum filament is 0.005 ohms.