A tungsten filament of resistance 0.350 ohm at 20 degrees C is heated to 2850 degrees C. Taking alpha as 4.5 x 10^-3 per degree C, what is its hot resistance?

1. Use R = R_0 (1 + alpha delta T) with R_0 = 0.350 ohm. 2. The temperature change is delta T = 2850 degrees C minus 20 degrees C = 2830 degrees C. 3. Compute alpha delta T = (4.5 x 10^-3 per degree C)(2830 degrees C) = 12.735, a pure number. 4. The bracket becomes 1 + 12.735 = 13.735. 5. R = (0.350 ohm)(13.735) = 4.8 ohm. 6. 12.7 ohm is the trap of leaving out the leading 1 in the bracket and dropping the factor R_0. 7. The result explains why a headlight measured hot reads a few ohms while the same lamp reads a fraction of an ohm cold. _Source: OpenStax College Physics (CC BY 4.0), Ch 20 "Electric Current, Resistance, and Ohm's Law", section Temperature Variation of Resistance_