There's no way of telling if the carbon is full and no longer doing anything.
Most people simply replace it every month, or don't bother using it at all.
You only need carbon if you have heavy metals or chemicals in the water, and if you do, then you should replace the carbon every week. use an "activated carbon" or highly activated carbon". However, if you don't have chemicals or heavy metals in the water, there is no point using it.