To what Celsius temperature must a copper wire starting at 20.0 degrees C be raised to double its resistance, if alpha is 3.9 x 10^-3 per degree C?

1. Doubling means R = 2 R_0, so R_0 (1 + alpha delta T) = 2 R_0. 2. Cancel R_0 to get 1 + alpha delta T = 2, hence alpha delta T = 1. 3. Solve for the change: delta T = 1 / (3.9 x 10^-3 per degree C) = 256 degrees C. 4. That is the change, not the final temperature. 5. Add the starting value: T = 20.0 degrees C + 256 degrees C = 276 degrees C. 6. 256 C is the trap of reporting delta T and forgetting to add the 20.0 degrees C starting point. 7. 532 C would follow from doubling the final temperature rather than the resistance. _Source: OpenStax College Physics (CC BY 4.0), Ch 20 "Electric Current, Resistance, and Ohm's Law", section Temperature Variation of Resistance_