In which rhythm do the P and R waves have regular intervals but are independent of each other?

In a third-degree AV block, also known as complete heart block, there is a dissociation between the atrial and ventricular activities. This means that while P waves (representing atrial depolarization) can occur at regular intervals, they are not coordinated with the QRS complexes (representing ventricular depolarization). The P waves continue at their own intrinsic rate, while the QRS complexes are generated independently, typically at a slower rate from the ventricles' escape rhythm. The result is that the intervals between the P waves and the R waves (or QRS complexes) appear regular, but they do not have a direct relationship with one another.

This characteristic of having independent rhythms makes third-degree AV block distinctive, as it demonstrates a lack of communication between the atria and ventricles, leading to two separate and regular rhythms occurring at the same time.