Database Connections

I am a S/W Developer, new to Web/WordPress programming. I know that a database has a finite number of connections available. Now, lets say I have a blog that displays a simple post. The way I expect things to work is that a person gets on my site. A database connection is opened, the post is retrieved from a table and then the connection is closed. This would allow a large amount of people to view my site at the same time and leave my site open all day. I get feeling that using the $wpdb means that a connections is open all the time. I hope this is not the case. Could someone please explain. Does a connection get closed when $wpdb goes out of scope?
Thanks