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Connect single pole load to double pole breaker
Can I connect 120 volt 30 amp single-pole load to 30 amp double breaker?
Isn't a 30 amp double pole breaker is same as two 30 amp single pole breakers stuck together, so I can put 30 amps on each leg?

Correct answer:
Rule of thumb: The breaker is rated for total amps.
A double pole breaker is 2 single poles with a joined handle. Yes.
The transformer delivers 30 amps on one leg and the 30 amps returns on the second leg, then it reverses direction.
Always put your 120 volt loads onto a single breaker for correct protection.

If you totally loaded a panel up with only single pole breakers you can put 200 amps on each leg?

Correct answer: No
Rule of thumb: The breaker is rated for total amps.
200 amps on each leg would be 400 total amps.
200 amp service has total 200 amp, or 100 amps per busbar (per leg) if you want to think of it that way.

A 200Amp 120/240Volt panel will only draw 200Amp, weather your dealing with 120Volts or 240Volts. If you draw 400Amps, the main breaker will trip.

Can I put 100 amps on one leg, and 5 amps on another leg?

Correct answer: No
The busbar cannot be overloaded on one leg, no matter 120-240 single-phase or any-voltage 3-phase.
The phases must be balanced within percentages.
An unbalance load will put the power company's transformer out of phase. You will not have the correct waveform on your electric service.
Question: Are both sides of the breaker 30 amp or one each one of them 15 amp ?

Answer: I had that discussion with a guy and did some research on electrician forums... which was a battle over sine waves and ultimately inconclusive.

Then I remembered reading an industry .pdf that said you can make a 240 breaker by combining 2 single-pole breakers, but that code requires you to install a 'common bar' between the breaker so if one trips, then the other breaker also trips...
Then I remembered the oscillating (sine wave) nature of electricity, where AC power reverses the direction of electrons 60 times per second... over and over and over... and how the voltage rises and falls as electrons come to a stop, reverse direction and accelerate the opposite direction... yet the average voltage is always above zero, and the oscillations happen so fast that it is not a noticeable factor for electricity as we humans use it.
Then I remembered that each leg of a 240 volt circuit is out-of-phase with the other leg.... which means the sine wave for one leg is mirror of the other leg... and the load receives more sustained power ...which is why we use 240 volt instead of 120 volts... because it is more efficient. This means each leg is delivering power to the load, and thus is independent of the other leg. Of course that is true because the electrons travel back and forth on the wire... and so one leg is pushing electrons when the other leg is pulling electrons ... this increasing total power, and this can be represented by the formula E = IR, or power (watts) = volts x amp. The formula shows if you have 30 amp, and change the voltage from 120 to 240, then the power (watts) goes up, or the amps (heat loss on wire) decreases.
... the final conclusion... the answer is that both breakers are 30 amp... because both are pushing and pulling electrons down the wire, like pedaling a bicycle with two legs instead of one.
... so yes... the answer is that both breakers are 30 amp.
Figure volts amps watts
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Refer to chart above.
1500 watt element.
12.5 amp @ 120 volt
or 6.3 amp @ 240 volt
So the amp rating drops by 1/2 for same wattage load.
This means that 240 volt breakers are designed to handle large appliances that cannot be supplied by 120 volt.
To illustrate how much more power 240 volt supplies to an appliance, we use the 4500 watt element with a rating of 240 volt.
When connected to 240 volts 30 amp double breaker, the element heats 16+ gallons per hour.
When same rated element is connected to 120 volt, it heats 1/4 the amount of water per hour, and a smaller breaker can be used. 
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