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I'm building a simple intrusion alarm system with a piezo buzzer fed by a 9V battery, I have a switch to activate/deactivate the alarm, and a trigger (like a switch) connected to a tripwire so if someone goes through the wire the alarm is set off.

My question is which of these configurations (A or B) is better in terms of saving battery life (so that the battery lasts longer if there is never an intruder), is there even a difference between the 2 configurations. I'm a newbie.

Conf A:

Configuration A

Conf B:

Configuration B

Which one would you use?

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In an open circuit, no current flows, so the battery should last as long as its normal shelf life (i.e. not in use). Both configurations are effectively identical.

To answer your question "Which one would you use?" Since they are electrically equivalent, I would use whatever one was more convenient and matched the physical layout. (To avoid having to run extra wire, for example.)

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Is the battery being drained?

Yes. Yes it is. By it's internal self-discharge rate. See How do I calculate the self discharge rate of a lead acid battery?
Nothing you can do about that, other than use the battery before it can discharge itself first.

Which of these configurations (A or B) is better in terms of saving battery life (so that the battery lasts longer if there is never an intruder)

Neither is better.

is there even a difference between the 2 configurations. I'm a newbie.

There is no difference. A disconnected series circuit is disconnected, no current can flow (not getting into high voltage and arcing across air gaps).

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There is only a single simple circuit and "trigger" breaks it in both instances. Both circuits are equivalent even though the components are in different orders.

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