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?)

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

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

The temp coefficient of copper is 0.00386 per unit Celsius.

To find the temperature at which the resistance of a copper wire doubles, we need to use the temperature coefficient of resistance. The temperature coefficient of resistance for copper is typically given as 0.00428 Ω/°C.

We can use the following formula to calculate the new resistance (Rt) at a given temperature (Tt):

Rt = R0 * (1 + α * (Tt - T0))

Where:
- Rt is the new resistance
- R0 is the initial resistance at temperature T0
- α is the temperature coefficient of resistance
- Tt is the final temperature at which we want to find the new resistance

Given that we want to double the resistance, Rt = 2 * R0

To find the final temperature (Tt), we can rearrange the formula and solve for Tt:

Tt = (Rt / (2 * R0 * α)) + T0

In this case, if we neglect any changes in dimensions, and assuming the copper wire follows the typical temperature coefficient of resistance:

Initial temperature, T0 = 20.0°C
Initial resistance, R0 = R (unknown, to be determined)
Temperature coefficient of resistance, α = 0.00428 Ω/°C
Final resistance, Rt = 2 * R0

We need to determine the value of R0 first. For that, we need more information about the wire or the specific situation. The question doesn't provide the initial resistance or any additional details to calculate it.

Regarding household wiring, under ordinary circumstances, the temperature of the copper wire doesn't reach levels where the resistance doubles. Copper is a good conductor with a relatively low temperature coefficient of resistance, so the change in resistance due to temperature variations is usually negligible.