I am looking for an Android application that can show the battery charging rate (e.g. in mA).
Free is better, but paid OK too.
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Battery Monitor will show that.
It has the ability to show it as a widget as well as in-app. It's also free (with ads)
It's pretty simple to use. I only used it for a short while but it does what you need.
The feature to show charging rate is a free feature.
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CurrentWidget also provides the charging information as a widget, and is also free.
CurrentWidget can also stay in your notifications bar to provide information, as well as provide alerts when the phone is using above a certain amount of power which I liked. Didn't really have any cons about them when I was using them.
Another popular alternative: Ampere.
Measure the charging and discharging current of your battery.
Alerts on device
Alerts on Android Wear
Galaxy Charging Current Free is another app that will show the battery charging rate.
Works on my SGS3.