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Is it possible that the battery uaH might decrease. A month back when I started using the Xperia z, the battery uaH found by *#*#service#*#* increased from 2370000 to around 2380000 but now it's back to the previous level 2370000, can anyone explain this?
Well, the Xperia Z has got a 2330-2400mAh battery. Don't know why the service menu is telling you anything else. This is hardware related so it won't change.
I assume the phone tries to calculate the battery capacity from the time to discharge under known load and is probably only approximate which is why it changed. 2370000uAh is the same as 2370mAh so your battery is within expected range.
Tell me, and what input current from a battery XperiaZ?