However, the amount of resistance dissipated by a portion of a collection of series-wound resistive wires will be the square of the line voltage, multiplied by the resistance of the portion, divided by the square of the total resistance. Thus, if a small portion of the wire is thinner than the rest, its higher resistance will reduce the amount of power dissipated by the rest of the wire, but increase the amount of heat dissipated by itself.

The most extreme case would be an infinitesimally-short section of wire being so thin as to have a resistance which equals that of everything else put together. In that scenario, since the total resistance will be twice what it would have been without the thin spot, so the total power dissipated will be half. On the other hand, half of that reduced total power will be dissipated in the infinitesimally small section of wire. If the whole toaster would have consumed 500 watts but for a small very thin spot in the wire, that thin spot could dissipate 125 watts–enough to get very hot.

I think I could make a toaster.

Assuming you used an oven to bake your bread, you already have a toaster.

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http://www.cbsnews.com/stories/2009/06/25/national/main5112597.shtml

I think this is the exact same statements I was making, without going into extra technical details. Less resistance = Less heat in this configuration.

I was never saying they would change the line voltage, I was saying there would be voltage drops through the circuit down from the line voltage and this is where the heat is generated. The voltage drops are due to resistance so here more resistance = more heat.

My real point was to disagree with #28 who asserted that the thicker wires would generate more heat and they presumably under some tension he doesn’t describe would get thinner to the point where they would generate less heat.

For the amount of power needed to operate a toaster, for all practical purposes, the line voltage stays constant. They select a value of R for the heating element that provides the required heat.

For example, if they want a 1000W element at 110V, they would solve for the required resistance.

R = E^2/P 110^2/1000 = 12.1 ohms

The wires that carry the electricity to the heating element will be big, have less resistance, less voltage drop, and generate less heat. It’s the element that does the work and the element has to be designed for the voltage that will be applied. To change the voltage would require a transformer which is expensive and heavy.

For the design of a toaster I’d say R is fixed rather than E. You probably want to have R set such that I < 5 Amps (so not to blow a fuse). In that case Power is fixed and the heat generated comes from the places with the biggest voltage drops in the circuit which correspond to where there is the most resistance.

I am a patent lawyer, former scientist, and often hear about how something is “obvious.” Of course this statement is always made from the perspective of having the thing in front of you. Just knowing that something exists is a bigger step than many people realize.

#29 Mike

thicker means less heat not more. Thicker gives a wider path for the electricity to flow through, thus less resistance and less heat. So if the material somehow got thinner it would be unstable rather than self regulating

You’re correct that bigger wire is less resistance, but you’re wrong that more resistance makes for more heat.

I=E/R and P = I * E

I = current in amps
E = voltage in volts
R = resitsance in ohms
P = power in watts

Assuming voltage stays the same (which it does at your wall outlet), increasing resistance decreases current. Since power (heat dissipated) is proportional to current, heat decreases.

Using regular sticks for the frame and cord made of some easy to use fiber*, I’d weave two squares of about five inches by five inches with half an inch or so between the cords. Attach a long stick to the bottom of one of them. That one is now “the bottom one”

I’d put “the top one” on top of “the bottom one” securing at one side with more cord*

I’d dip the whole thing in a bucket of water or a lake for good measure.

OK, now I’d take a piece of bread, put it between the two squares and then use more cord to close the thing around the bread and keep the top on.

I could hold it over the fire and as long as it didn’t get too close, the bread would slowly turn to toast. I’d have to hold it a little higher than one would hold a marshmallow, and it would take a bit, but I bet it would work.

IMHO, this guy’s issue is his definition of the word “toaster”

CC

*Or vines, if I sucked at making cord

This one item would be difficult to substitute for and if you don’t have even thickness over all 80 feet of it your toast won’t cook evenly. Thicker wire = less resistance = less heat.

“Well, just ‘cuz command economies are horribly inefficient doesn’t mean they’re not better than capitalism!”