The heat source has to be dimmed and not just switched on and off there are several reasons for this.
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Unlike humans reptiles cannot move away from the vivarium if it gets too hot or cold. Accurate and maintained temperature control of the environment is key to the health of the reptile. Heat loss from vivariums especially glass ones is a problem.
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Unlike humans reptiles thermoregulate in order to digest food and this requires them to have a constant temperature which varies depending on the animal.
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Some of the hot spots in vivariums are achieved using bulbs and not ceramics, how annoying for the reptile and the human inhabitants would a light switching on and off be.
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These vivariums are heated 24 hours a day 7 days a week with temperature differences between day and night and also between normal and breeding seasons. It is more efficient to control the heat source using a dimming technique that it is switching them on and off. after all there is a recession on.
I agree that any circuit that uses AC power is lethal and I also accept that I don't know an lot about this subject, but I wasn't born a computer programmer or reptile keeper either I had to start and learn somewhere.
The idea of asking for help and understanding in this area was to ensure I understood what I was trying to achieve before attempting it in a controlled manor. It would be foolish of me to just plug some components together and see what happened. I was asking for help in understanding how this circuit was working.
I accept that a transformer type circuit is maybe a better way to go to provide DC power, but it still will not negate the need for me to use dimming circuits to control the outputs.