This is a general answer, not specific applicable to the situation in the USA.
There are several types of radars in use to monitor airspace.
Basically you can distinguish two classes of radar:
- Primary radar does not require the aircraft to carry a transponder, it is a form of non-cooperative surveillance.
- Secondary radar on the other hand requires the aircraft to carry a transponder; the transponder replies to interrogations from the radar. This is called cooperative surveillance.
Radars operate basically by line-of-sight, however due to atmospheric effects the radio waves follow the curvature of the earth to some degree. Aircraft flying low are quickly below the horizon, but aircraft at FL450 can be detected on secondary radar at ranges up to 300NM if the radar is operated for such range. Typically the range is less.
In general, the further the range that a radar needs to look, the slower it rotates. An airport surface radar may rotate as fast as twice per second, long range en-route radars can go as slow as once per 12 seconds. For typical TMA / TRACON use, 5 seconds would be in the right ballpark, for en-route 8 seconds will be about right.
The accuracy depends on the type of antenna, whether it is primary or secondary radar, and the distance of the aircraft from the radar head. The accuracy of the distance measurement are not so much affected by the range, and varies from about 5 meters to 300 meters. However, atmospheric circumstances can degrade these figures, especially at long range. The across beam accuracy is very much dependent on the distance from the antenna due to limited angular accuracy of the radar. The further you get, the worse the across beam accuracy becomes.