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If this is a single unit device, not a component of a system, then pull the battery out and arrange some way to reconnect the battery to measure battery current. If this uses a rechargeable battery, then you should also be able to see charging current.
Apply AC power for a short time. Measure battery voltage and current with AC power on. If there is a visual numeric display when AC power is on, then note whether that goes off when AC power is removed.
Remove AC power measure battery voltage and battery current. Leave AC power off. Sometime later, possibly 15 minutes, again read battery voltage and current.
Determine whether the battery is a recharagable type or not.
Lookup the battery specifications. In particular the slow discharge capacity in ampere-hours. Use your battery current measurement to calculate an estimated duration of operation for the battery.
Most primary batteries have a long self-discharge rate, like years. Most secondary batteries have much shorter self-discharge times. NiCd can be in the 1 month range. Lead-acid somewhat longer, but some lead-acid are quite a bit longer. Depending upon the load, the self-discharge may be dominate. CMOS memory chips are an example where self-discharge can be domoninate.
I once shipped a system with CMOS memory battery backed up with NiCd batteries. Parameter data was stored in the CMOS memory. The machine was never powered for a year, yet the CMOS data was still good when power was applied. The CMOS only required a few microamps to retain data. Even though NiCd retains a usable charge for only about 1 month there was still enough energy in the battery to retain the CMOS data.
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