> Is a 2,500 foot track circuit which operates at 100 hz practical?


I don't see why not, in conditions good for it at least. And as long as a "Double Rail" configuration is used, rather than single rail track circuits. Double rail circuits have insulated joints on both rails at both ends; propulsion current (if required) bypassing the joints through balanced impedance bonds) at each end; and it is designed with the right component values. But where most of my life's work was done, 2500' was longer than would ever be useful, mostly because of traffic density. This was also true in old overlapped ABS (The first kind). Really long track circuits were seldom needed due to the staggered placement of signals.

In my experience, single rail AC track circuits more than say, oh, 700ft and up; begin to become a pain in the neck. The longer they get, a nasty phenomenon appears on electrified track, that of current crowding; which is DC propulsion current spilling into the signal rail and thus all signal circuits; magnetically saturating out track transformers, relays, etc. This causes intermittent false occupancy and can also burn out the circuitry. Counter measures can be deployed, but at some point, it all begins to cost more than it is worth.

It will require more power to be injected at the transmit end, the longer the track circuit gets. And of course, one must pay attention to leakage currents between the rails, usually caused by sneak paths of less than 5 parallel ohms per 1000 feet of track circuit. 2000' would present a leak path of only 2.5 ohms, and so on. It is typically these leakage currents that are the most limiting factor in track circuit length; and they vary widely. Just try to detect a .060 or 1/4 ohm shunt with total leakage resistance anywhere near those figures. You would likely detect the leakage even with no train present. The longer the track circuit gets, the more likely this will happen in adverse conditions.

At higher frequencies typical of modern coded AF track circuits), total track impedance becomes major factor limiting length. Typically, those in the 5-7khz range are limited to about 1200ft. Those in the 2-5khz range a little better than about 2000ft. AF circuits in the 200-1800hz range, and power frequency track circuit can do Better.

One CTC installation I got in on briefly in the deserts of Utah, was using special pulsing track circuits purported to be capable of 15,000ft, using very unique (and patented) methods of overcoming track inductance. I never did get to see a track circuit that long actually work, before I had to move on to another assignment. But it was interesting to contemplate at the time.

But hey, I gotta run - though I am retired , the real "boss" calls.......