I am trying to understand wire gauge size vs current flow?

Question

I am trying to understand how wire gauge size relates to the current that will flow through it.

Lets say we have a 100 foot long, 16 gauge extension cable made internally of copper wiring.

After looking at a gauge vs resistance chart, I know that a 16 gauge wire will have 4.016 ohms resistance per 1,000 feet. So in this case, our wire will have a resistance of 0.4016 ohms (1000/10 = 100 ft).

Wall outlets in the U.S. supply 120 Volts. So does this mean that 292 amps of current (I = V/R, I = 120/0.4016) will flow through the extension cable when plugged into the wall socket?

If this is the case, then why do 100 foot 16 gauge cables have a device amperage rating of only 10 amps? What am I missing? Any help is greatly appreciated.

Answer 1

So if you short circuit your 100 foot cable, it will draw 292 amps, which should trip the breaker. That is not the point of current ratings, as short circuiting is not the point of an extension cord.

The extension cord is designed to have a load on the business end. What they are saying is that this load should not draw more than 10 amps, and the rating is based on power dissipation in the copper (i.e., heating).

Of course:

$$ P = I^2R $$

so a 10 amps and $R=0.4 \,\Omega$, thats 40 Watts (per 100 feet) heating the cord. According to then engineers, that's the acceptable limit.

Note that 40 daisy chained 16-gauge 100' cords would have a resistance of 16 Ohms. Using:

$$ P = \frac {V^2} R $$

they would make a 900 Watt heater, while drawing a 'safe' 7.5 Amps, when short circuited.