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Is it OK to supply a smoke detector with a separate circuit all by itself?
I am assuming you are talking about AC powered smoke detectors with a battery backup. It seems to depend on your location. In a NJ township where I have done some re-hab's they are required to be on their own circuit.
I have been told (no personal experience) that other jurisdictions require them to be on a shared circuit. They say this is so that you can't just flip a breaker to disable them.
I would check with your local inspector because they also have stringent rules about how many you will need, which will also need to be CO alarms and where they need to be located.
Here's an interesting link related to AFCI's
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