Although this is still usually the case, many ISP's are now reissuing your same IP address unless the link has been down for a certain period of (inactive) time.
Historically, you used to be able to merely power your cable modem/router off for 5 seconds and then flip it back on and then your ISP would automatically give you a new IP address. Please note that reconnecting does not work for all routers/cable modems, nor does it work for all internet service providers.
