A tungsten filament of resistivity 5.6 x 10^-8 ohm m is a cylinder 4.00 cm long with a cold resistance of 0.350 ohm. What is its diameter?

1. Rearrange R = rho L / A to give A = rho L / R. 2. Substitute with the length in metres: A = (5.6 x 10^-8 ohm m)(4.00 x 10^-2 m) / 0.350 ohm. 3. That gives A = 6.40 x 10^-9 m^2. 4. For a circular cross-section A = pi D^2 / 4, so D = 2 times the square root of (A / pi). 5. D = 2 times the square root of (6.40 x 10^-9 m^2 / 3.14) = 2 (4.5 x 10^-5 m) = 9.0 x 10^-5 m. 6. 4.5 x 10^-5 m is the radius, and forgetting the factor of two is the commonest slip here. 7. 6.4 x 10^-9 m is the area value carried over with the wrong unit attached. _Source: OpenStax College Physics (CC BY 4.0), Ch 20 "Electric Current, Resistance, and Ohm's Law", section 20.3 Resistance and Resistivity_