2009 Track Circuit Question

[PJW]

In the type of simple calculations asked in the IRSE exam, the whole point is that the rail series resistance must be considered negligible- indeed at dc and low frequency ac then the rail resistance is indeed so in practice (large cross sectional area of steel which is reasonably good conductor), but it is the intermediate bonding, rail jumpers and track leads that can become significant.
If the rail resistance (impedance for ac of course) is not negligible then the voltage on the rail will vary along its length and the whole simplicity of lumping all the leakage currents distributed along the entire length as if it due to a simple "ballast resistance" between those rails isn't applicable.
One is then faced with a calculation involving differential calculus which I forgot how to do more than 30 years ago and becomes an exercise in mathematics not railway signalling.

[quote='MJB' pid='1065' dateline='1254744007']
I raised the issue with the invigilator during the exam, he came back to me and said that there was a worked solution to the question, and said he couldn't comment as he hadn't done the maths himself, which is fair enough, but does suggest a typo rather than a dirty trick.

If the feed resistance was 10 ohms (not 100 ohms), and you did assume 9 ohms for coil resistance, and that rail resistance refered to the loop resistance of the rail and that ballast resistance sits entirely in parallel with the coil (which on relflection it must do as the conductivity between rails will vary along the length of the track circuit and be dominated by the specific point along the track ciruit with the lowest resistance between rails, so the concept of a "ballast resistor" is a bit abstract, yet alone specifying a dimensioned value per KM) then the question was very simple, hence only 10 marks. (or was it 15).

Anyhow, I'm sure it should be Mod 1 I'm more worried about than Mod 5

I also tried this question assuming feed resistance as 10 ohms and 9 ohm for relay coil but I am not sure how to consider rail resistance in the track ckt calculation.
could anyone help me to figure it out?
Thanks