# Temperature Increase of a Wire

1. Jun 30, 2008

### ejandres

So they decided to give me an electrical problem at work, and I am completely lost. They're worried about 120V from the wall crossing over onto a 22 AWG wire and causing it to heat up. Is there a way to calculate temperature versus time for this situation? The length of the wire will change with each installation, so we were going to normalize it to per foot of wire.

2. Jun 30, 2008

### ejandres

I also should have mentioned, we're assuming a copper wire in all installations.

3. Jun 30, 2008

### ejandres

I've gotten some work done (not 100% sure it's correct though): I got a resistance of 0.0165 ohm/foot for AWG22 for copper from a copper wire resistance table. Using this and the 120 V from the wall, I calculated a power of 872,727 W/ft. From here, is there a way to determine the temperature of the wire? And how this would vary with time?

As I said, assuming a pure copper wire, and also standard PVC insulation.

4. Jun 30, 2008

### Integral

Staff Emeritus
I am not sure how you came up with ~900kW but that just can't be right. You have not given a key factor. What current is being carried by the wire? Without knowledge of the current or the load you cannot calculate power.

Going from power to temperature is not easy, there are just to many environmental factors which need to be accounted for.

5. Jun 30, 2008

### nucleus

There are electrical codes in place that usually must be followed in order to add wiring. These codes have determined allowable voltage drop etc for conductors and how much current you are allowed. It depends on type of insulation, if it is a single conductor or run with others, ambient temperature, and many other factors.

I think you should either get a current copy of your code or employ the services of a qualified electrician to do what you are doing.

Cheers

6. Jun 30, 2008

### mgb_phys

It sounds like you have calcualted it for a direct short circuit, ie 120V across one ft of wire, you need to calculate it for 13Amps or whatever the max the circuit is supposed to take.
As nucleas says, there are codes for each wire type and current, which also take into account the position of the wire, so you are allowed to have more current and therefore more heating in a single wire inside a brick wall than in a bundle of wires in a conduit for example.

7. Jul 1, 2008

### rolerbe

There are a couple of things not yet mentioned that may need to be considered. I get from you problem description that you are talking about heating of the 22awg (signal) wire from a nearby 120VAC (power) wire. So you are talking about an 'induced' current in the signal wire due to either RF or magnetic coupling.

First, you can simply measure the induced current in the signal wire as a function of distance between the wires and current load in the power wire. It will be pretty small. Second, you can calculate the max allowable induced current from the resistivity (about 53Ohms/ft). 22Awg is rated to almost 1Amp for power. This is an awful lot, but may change for different insulations which are the actual limiting factor.

I would think the bigger problem than heating would be the induced current itself interfering with the electronics that the signal wire is connected to.

8. Jul 8, 2008

### zmrbill

The others are right, consult the NEC table.

The other concern is that the protection circuitry (fuses or circuit breaker) opens before the wire becomes a plasma ball in the case of a fault.

If this is a customer installation there could be legal implications!

Never underestimate the complexity of even simplest AC power circuit.

Bill