Question

To what temperature must you raise a copper wire, originally at 20.0°C, to double its resistance, neglecting any changes in dimensions? (Does this happen in household wiring under ordinary circumstances?)

Answer 1

R=Ro+Ro*a*(T-To)
(2Ro-Ro)/Ro=a*(T-To) we want to double resistance. For example if our initial resistance is 10, we want R to be 20, therefore R=2Ro. (2Ro-Ro)/Ro=1, so

1/alpha=T-To divide by alpha
(1/alpha)+To=T add To to both sides
So To=20C. Alpha from my old old physics book for copper is .0068. Therefore 1/.0068 is 147+20=167C

Answer 2

This would not happen in household wiring because of circuit breakers.

Answer 3

The temp coefficient of copper is 0.00386 per unit Celsius.