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Hydraulic Magnetic circuit breakers work this way

Magnetic circuit breaker are basically bistable relays in which the mains currents passes through the relay's coil, and the mains also passes through the contacts.
Huhhhh? go below:

Bistable relays have two stable positions, which are positions in which the relay will stay even after coil is no more energized. See image at left
This is done thanks to a magnet who provides the necessary force on the contact. Two magnetic paths are possible, and the relay switches from one to the other when suffisant force is appllied onto the armature. This force can come from coils, user accessible button, thermal deformation of a piece of metal, depending on the use.

Af for the magnetic circuit breaker, in its idle working position, the contacts are closed: current passes through the coil then through the contact and powers your equipment.
Current passing through the coil creates a force (pulsating 100 or 120 times/second).
When current grows over a threshold, this forces becomes high enough as to make the armature switch to the other position. Clack!
The contacts are now open, no more current passes, and the retaining force nulls. The contact stay open, since the magnetic path has now changed.
To get back to working position, you will by hand push the armature to the closed contacts position. Click!
You can combine this breaker with a thermal mechanism, many possibilities exist. For example, the heat generated in the coil can move the armature by a deformable bilayed piece of metal (as in thermostats). Or above a threshold, the magnetic properties of the armature can change and "short" the magnetic path, and so the magnet makes the breaker to act.
Maybe , you have heard of magnetohydraulic breakers or names like that. They are just magnetic breakers in which the armature movement are heavily damped by an hydraulic damper. The aim is to slow down the really fact action of pure magnetic breakers.
Most household appliances breakers are of this type (often combined with thermal action)

Above the Hows, the Whys:
Magnetic breakers react in a matter of milliseconds to an overcurrent above their threshold. So, would the current be several times or several dozens of times the rated current doesn't change much in their reaction time: difference between 1millisecond and 4 milliseconds is of concern for use humans.
Thermal breakers on the other side will take a much longer time, since they have to heat the coil surrounding before being able to act.
Hydromagnetic breakers are in the middle way: they act in a matter of tenths of seconds instead of milliseconds.
Example with a thermal breaker:
At 1.2 their rated current, they switch in one half hour.
At 2 their rated current, they switch in 60 seconds
At 5 their rated current, they switch in 10 seconds
At 10 their rated current, they switch in 2 seconds
At 20 their rated current, they switch in 1 second
So, their use depends on the application. For motors and linear power supplies, you can use a thermal brk rated at the max steady power, and/or a magnetic breaker rated at 5 times the max steady power.
A simple hydromagnetic breaker will work great with linear power pupplies (audio system). Those, when powered up, do suck about 5 to 10 times their rated power for 10 milliseconds (the time to charge the storage caps). A purely magnetic breaker rated at the normal steady current would trip. An hydromagnetic won't, but would trip in case of a short or an overload in a time short enough as to protect your equipment. A thermal alone would be too slow to protect your equipment.

Magnetic and thermal breakers are often combined. And even combined with the on/off switch, which is an appealing feature (in pro audio, it's much better to push the on/off rocker back to ON than change a fuse in the middle of a venue because the electric intallation of the customer is crappy and is prone to overvoltages)
I do like combined switch/magnetic/thermal breakers.



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