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Size 14 wires attached to 200 amp breaker

14 gauge wire connected to 200 amp breaker
Connecting any small wire to a 200 amp breaker is totally unsafe ... fire hazard.

Electricity can be thought of as heat. Amps, or the ability to do work.

Circuit breaker trips when it gets hot  ,,, the causes for overheated breaker range from too much voltage on wire, short circuit, loose wire connection at breaker, loose breaker, loose wire at switch, failed switch etc.

Too much heat and breaker trips.
If the breaker is rated too many amps for the wire, the wire cannot carry enough heat to trip breaker, so the overheated 14 gauge wire will not trip the 200 amp breaker. Wire inside wall gets overheated, it causes a fire.
That's why it's important to match breaker and wire size;
14 gauge wire should have 15 amp breaker
12 gauge wire 20 amp breaker
10 gauge wire 30 amp breaker
Resource:
Wire size chart and Color code for wire

If 14 gauge wire is connected to 200 amp main breaker, followed by an open short (for example: loose wire or failed switch, where electric power jumps to the ground wire or the neutral wire or nearby human or piece of conductive metal), the full 200 amps will race down the 14 gauge wire.
The wire won't only get hot, it will catch fire inside the wall. It will pop like a firecracker.
If the correct breaker was used, the heat caused by a failed switch would cause 15 amp breaker to trip before the 14 gauge wire gets hot, but the 200 amp breaker will not trip before the wire catches fire.
Always use correct size breaker and wire.
Ground wire can help protect you and your appliances, but only if circuit breaker and wire size are correctly matched.
You can prevent electric shocks and damage by using GFCI or arc fault breakers.
Resource:
How to wire GFCI
If your appliance has 3-prong grounded plug, then that appliance can have short circuit that travels to the outer shell of appliance, and this short can kill you if appliance is not grounded.
If that appliance is connected to oversized breaker, then the risk of injury and fire are extreme.

That's why the national electric code specifies wire size and breaker rating, and why there are UL rated appliances. These things are important rules and best-practices for electrical devices.
Many countries do not have codes, or the codes are frequently unfollowed by tradesmen who don't have available materials and customers who lack money needed to meet safety requirements.
Resource:
Basic wiring shown on my website

The ground wire is connected to outer shell of appliance, and travels back to main breaker box, and then to ground rod outside home.

For example water heater recirculation pump has 3-prong plug. If recirculation pump gets a short circuit, then the ground wire will carry amperage safely away from pump, and away from water pipes.
Remember the recirculation pump is connected to your bath and shower.

If the ground fault is slight and not large, then breaker will NOT trip, and ground wire releases the small current into ground rod located outside house near main panel ... and it is generally safe to touch recirculation pump.

If the ground fault is large enough, it will begin to pull more current through shell of appliance and into ground wire and down to the ground rod, and that current will overheat wire at breaker, and breaker will trip. It will happen very quickly, but until breaker is tripped, the live current is available on the outer shell and can still kill you.

If you do not have ground wire, and recirculation has large short, and you touch recirculation pump while standing on bare ground, or while touching water pipe, or leaning into metal washing machine, or taking shower etc... you can fry like a fish, as current finds easiest path down to ground.

This is why grounding is important.
IF you have GFCI or arc-fault breaker on the circuit, then the slightest ground will
trip breaker.
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.
Resources:
Figure volts amps watts
Formulas for ohm's law
What is electricity
How a generator works

Orange 10 gauge 30 amp breaker


Orange/ #10 gauge for for 30 amp circuits including water heater
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Yellow 12 gauge 20 amp breaker


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White 14 gauge 15 amp breaker


White/ #14 gauge wire for 15 amp
with ground
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NMB is house wiring
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Copper ground wire
Use same size as other wire in circuit

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Resource:
Why you need ground wire
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