I have an alarm clock with an LED display that has a 9v battery back-up. If I leave the battery plugged in will that use up battery power?

The alarm clock offers a 9v battery back-up. If I lose power, the 9v battery will keep the alarm clock running so that it wakes me up on time. If I leave the battery installed, will it automatically use battery power, whether the alarm clock is plugged in or not? Or would it only use battery power when I lose... show more The alarm clock offers a 9v battery back-up. If I lose power, the 9v battery will keep the alarm clock running so that it wakes me up on time. If I leave the battery installed, will it automatically use battery power, whether the alarm clock is plugged in or not? Or would it only use battery power when I lose electricity? Intuitively, it would seem that it wouldn't use battery if the alarm clock remains plugged in, but is that wrong?
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