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say we have a RL circuit with an direct current source (ie.battery), we have a second solenoid encloses the first coil (like transformars), the second coil is open ended. Now, we have switch in the first circuit. whenever the switch is opened, due to high rate of change magnetic field flux in the first coil, there is a huge induced voltage produced in the second circuit and since the second circuit is open, there will be spark.
Untill this point I have no question, but what I dont understand is, what woould happen in the switch? I doubt there should be spark through switch too since the idea is still the same as in the second circuit

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Any time you open or close a switch, there's a possibility of a spark (or arc) between the contacts. That's because as the switch closes or opens there's some point where the contacts are very close together, but not touching, so that the field between them exceeds the breakdown voltage of the air, producing a spark. This effect is one of the main limiters to the lifetime of a switch, since these sparks damage the surfaces of the contacts, eventually increasing the resistance of the switch in the closed position until it is out of spec.

When the switch is connected to an inductive load, this effect is stronger during the disconnect operation, because as the switch disconnects, the current through it will decrease, which can produce a large voltage (due to back emf in the inductive load, as mentioned in another answer) across the switch, so that the spark in the switch can be produced with a greater separation between the contacts, and sustained longer as the contacts move apart; thus causing more damage to the contacts.

With the circuit you describe, where a spark gap is connected to the secondary of a transformer, with the primary powered through the switch, the presence of the secondary circuit will actually reduce (but not eliminate) the arcing at the switch, because the energy lost in the spark gap on the secondary won't be available to maintain an arc in the switch.

If you are designing the circuit you described, called a flyback circuit, you will choose your switch carefully to be sure it can withstand the back-emf produced by the transformer over the lifetime you need it to operate.

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Yes, there could be sparks but not necessary, in circuits with inductance or capacitance there is also a phenomena called back emf, that try to resist any change in current. Hence, if the values match up, it can so happen that the transition from zero current to max current happens very slowly so that no sparks happen.

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