Question

The wire typically used to connect to 120Vac wall receptacles is #14 AWG solid copper Romex. If the initial temperature of the wire is at 35°C, what is the 12t needed to melt the wire? (Refer to section 26.23 in Wildi)

I²t=11.5E4 A2 log₁₀( 234+θm/234+θ₀)

If the circuit breaker failed to trip feeding this receptacle allowing 50 A to be continuously delivered into a faulty load, how long will it take the wire to melt?

Answer 1

To calculate the time to melt a #14 AWG solid copper Romex wire carrying 50A, we use the given I²t formula with 35°C as the initial temperature and 1085°C as the melting point of copper.

Step-by-step explanation:

To determine how long it will take for the #14 AWG solid copper Romex wire to melt when carrying 50A, given that the circuit breaker has failed, we use the given equation for I²t:

I²t=11.5E4 A² log₁₀( 234+θm/234+θ₀)

We're given that the initial temperature (θ₀) is 35°C. However, the melting temperature of the copper (θm) isn't provided directly, but it is known to be around 1085°C. Substituting 50A for I and rearranging the formula to solve for t, we get:

t = (11.5E4 A² log₁₀( 234+1085°C/234+35°C))/50A²