I would interpret as the 16 ga wire circuit had greater overall resistance. In a simplified system V=IR, if the voltage is constant then current is inversely proportional to resistance.

This is a really good experiment to learn the basics of Ohm's law and electricity. To advance a theory and have it proven wrong isn't bad, that's how we learn in science. Best wishes on this science project!

Ohm's law can be stated as V = I*R where V is the voltage in volts, I is the current in amperes, and R is the resistance in ohms.

Let's use ohm's law and determine the resistance of the shop vac:
V(wall) = I(shop vac)*R(shop vac)
118.40 volts = (10.72 amps)*(R).
Solving for R, R = 118.40/10.72 ohms = 11.04 ohms = resistance of the shop vac.

When you use the extension cord with the shop vac, the resistance of the extension cord wire is in series with the shop vac resistance so we modify the ohm's law equation a little. Using the 16 ga cord:
V(wall) = I* (R(cord)+R(shop vac)), or
118.40 volts = (9.93 amps)*(R(cord)+11.04 ohms)
using algebra to solve for R(cord),
R(cord)= 118.40/9.93 - 11.04 = 0.88 ohms

You can solve the above equation using the voltage and current values measured for each extension cord and determine each cords resistance.

The added resistance of the extension cord is why the current draw of the shop vac with an extension cord is lower; the resistance of the extension cord with the current passing through it causes a voltage drop to occur via ohm's law: V(drop) = I(total)*R(cord). Notice that the large wires (lower gauge number) have lower resistances and lower voltage drops. This is important in regards to your heat damage question.

Heating in wires is due to lost electrical power in the wires as the electricity is passing through the wire. Power in electrical terms is volts times amps or Power(heat) = P = V*I where V is the voltage drop along a wire and R is the wire's resistance. It's not always easy to measure the voltage drop along a wire (you have to make a measurement at both ends), but the current in a single wire circuit is the same everywhere, so we can measure the current (I) at any location that is convenient along the wire, and if we know the wire we're using, we can look up the wire resistance in a reference table. Using ohm's law and some algebra we can simplify the power equation:
P = V*I, but V = I*R from ohm's law, so
P(heat) = (I*R)*I = (I^2)*R =(current squared times resistance). Using this equation for power and looking at the extension cords, the current squared for the larger-wire cords is a little higher for the bigger cords, but the resistance is much lower, so the bigger cords generate much less heat, therefore there's much less risk of them overheating and starting a fire.

Hope the above makes sense to you. Feel free to contact me on my personal email with any particular questions.

Rick
formulaross@sbcglobal.net

to put that in simpler terms, there is more conductive metal in the larger cords, so the current flows more freely. the freer the current flow, the less is lost to heat.

but if your son shows the equations above, it will improve his grade! if he can explain it that is.

Also keep in mind, resistance is temperature dependent, so has the wire heats up the resistance goes up. While the total power goes down, a higher percentage of the power is used to heat the wire, instead of turning the motor.

As soon as the load becomes a motor things get compicated fast.
Most shop vacs use 'universal' or brush type motors. They simply run slower as the voltage drops from losses in the wires feeding them. They are not simple resistive loads and do not obey the simple resistive Ohm's law equation.

If you had an induction motor they actually pull more current as the voltage falls and they attempt to maintain output power. If the load is very light a decrease in voltage may have no effect on current, but if they are heavily loaded the current will increase almost immediately. The motor windings then cannot support the higher current and overheat and burn out.

To simplify, Ohm's law (I = E/R) shows us that current is inversely proportional to total circuit resistance. We also know that in a series circuit, the current is everywhere the same. The smaller wire has a higher resistance, so the total current is lower.

The reason that undersized wires are unsafe is that too high a proportion of the power (Watts) consumed is dissipated in the wire, instead of in the appliance. Just as a 100 Watt bulb produces more heat than a 25 Watt bulb, dissipating more power (Watts) in the wire may lead to more heating in the wire, producing an unsafe condition.

Good for you, encouraging scientific investigation for that kid!

In reference to brickeye's post about the motor load complicating things, maybe you should try the experiment again with a 1500 watt space heater as the load. This would be purely resistive and not complicate the calculations by being an inductive load like a motor.

but was the load on the vac constant?
the freer the air flow on a vac the current changes...
being a motor the load makes a difference. brickeye's is right the load makes a difference on the circuit. an induction vs capacitive vs resistive make a difference in AC math..

-dkenny

Even a typical space heater has a motor, though it's a very small part of the load. A radiant type heater with no fan will be a purely resistive load. So will a row of big light bulbs.

Back in the day, you could buy 750, 1000, and maybe higher Wattage heater coils that screwed into Edison base sockets. These were great for such experiments. I haven't seen any of those in at least 20 years, and even then they were VERY old stock.

It might be even simpler to understand if you turn davidandkasie response around...

Smaller Wire = Greater Resistance.
Greater Resistance = Less Current (Amps).

Thanks for the very informative and educational replies-- for both my 12-yr. old child and myself. There are a number of finer points noted above that I'm not sure he fully grasps, but he certainly has a better understanding of some of the basics of resistance and current.

Thanks again!