Why is it that when my cell phone is plugged into the charger, after being dead, it still doesn't have power for a while?

If you know me, you know my cell phone is dead about 1/5 of the time.

When I plug it in to the charger, it still doesn’t “wake up” right away.

Shouldn’t the phone get power immediately from the charger without having to wait?

I have a Samsung Galaxy 4, but I used to have a Blackberry and experienced the same thing.