The C172 Cockpit: Explained

I’ve been flying the C172 for some times now and I was wondering if the turn coordinator was functional.
I am asking this because I can’t seem to get the ball in the cage no matter how hard I go on the rudder.

I know this is a very stupid question, but what is the difference between

Master Alt

Master Battery

Standby Battery

I have always wanted to know when and how to use them

Anyone who knows more please correct me if I’m wrong. I haven’t been flying in a few months and I’m rusty on my vocab.

Supplies electric current to the electrical system when in the air while giving enough power to the battery

Provides electrics to the aircraft basically (basically a key of the car minus the engine starting)

“System will automatically supply electrical power to the Essential Bus for at least 30 minutes.”