I do not think that Peter's comments are far from the mark. I certainly think that one thrust of the question is to allow you to demonstrate typical parameters for the track circuit (eg what value would you expect for Vf?)
You have undoubtedly shown that you can model the inter-relation between the parameters.
I think that what you have shown is a mathematical proof for the general abstract case rather than some calualtions to show the examples asked for. It is difficult to say how the examiner would have interpreted this - they have often said that even if you do not quite interpret the question as they intend, provided that you demonstrate signal engineering knowledge, you may get credit.
The biggest thing that I would say is a problem is the interpretation (or lack of it) on the "reliable" operation. You have shown the algebraic condition for relative values when the relay will pick and drop, but have made no real comment on margins of operation and have assumed the ideal operation of the shunt. I think that you ahve written that Rs will be 0 for drop, although you have used the term R(infinity). This is not a normal operating parameter.
Don't be disheartened - you obviously understand the maths behind it, just make sure you put down the context and the typical expected paramenters and describe the operation in some words. Maths can describe most things, but don't be afraid to use words to relate it to the real world.
Peter
You have undoubtedly shown that you can model the inter-relation between the parameters.
I think that what you have shown is a mathematical proof for the general abstract case rather than some calualtions to show the examples asked for. It is difficult to say how the examiner would have interpreted this - they have often said that even if you do not quite interpret the question as they intend, provided that you demonstrate signal engineering knowledge, you may get credit.
The biggest thing that I would say is a problem is the interpretation (or lack of it) on the "reliable" operation. You have shown the algebraic condition for relative values when the relay will pick and drop, but have made no real comment on margins of operation and have assumed the ideal operation of the shunt. I think that you ahve written that Rs will be 0 for drop, although you have used the term R(infinity). This is not a normal operating parameter.
Don't be disheartened - you obviously understand the maths behind it, just make sure you put down the context and the typical expected paramenters and describe the operation in some words. Maths can describe most things, but don't be afraid to use words to relate it to the real world.
Peter