Share your experience!
Apologies in advance for my poor English...
Ok. This is weird.
i bought a Z5C for my wife, but I am withholding it fo test purposes because I own a Z3c... 
As per title, if I use it while charging the battery's charge drops or, at best, doesn't improve.
Before you ask...
I had already:
I don't' have strange applications running, I don't play games, mail synchronization is manual. It's like my phones are on perpetual holidays.
More over: I used it just to surf the web and take a dozen of shot with the camera set at 8MP, so nothing really challenging.
The phones back heats but not really that much.
Any idea?
With all the due respect, I don't think that is normal that a device has not to be used while charging to avoid charge dropping.
With Z3c I used to surf the web, watching videos or doing any kind of task while under charge and have the battery charge improving.
I've figured out that this is phone's processor is power hungry so It needs a more powerful charger than the one supplied with Z3c. If it's so, it's pity for Sony not to put the right charger in the box. Mine come with just an USB cable and nothing else.
Technical support told me that they do it because there are already so many chargers around and they want to be a "green company". A "green company" that wants to sell you the new 2 Ampere charger in addition to an already expensive device, rather than supplying you with the right one.
Sony used to be different...
Items in the box vary per region, also I've seen users in the UK posting that certain networks remove the wall charger, why? bc of what you stated, is your phone network branded or bought through a carrier?
As for using the phone while charging, I do it all the time, with the Z5, Z5 premium, Z3, and other Xperias, I only see this problem if I'm charging it through a computer or car charger and I'm using heavy games/apps or multitasking with several apps/games which will drain the battery faster than it can recharge, again, that's normal.
You can use the search bar and find posts like this
as you can see items in the box vary per region and even in the same country.
The device is unbranded and bought from Sony via Amazon. I don't know why but, from time to time, purchases in my country can't be made directly from Sony or are diverted to some online retailer, Maybe it has something to do with supplies.
Anyway I wrote to Sony and they replied that the Sony's box contains only an usb cable, while some carriers (like Vodafone) supply charger and headphone too.
The point is that they don't supply this device with the right charger, whether a user play games (which is not my case) or surf the web. And this is awful.
I would like to open a case with the technical support which I discovered to be, at least here in my country and during the last few months, less than unuseful. So I prefer to devolve my time here on the forum.
This is rather strange, have you contacted amazon regarding the items in the box?