aaiyar:
What you're attempting will not work.
In a 24 VAC (volt alternating current), R is the live conductor. C is the return path for the current back to the transformer. My terms are probably all wrong, but when I took physics 30-odd years ago, I think it would have been called the common equipment ground conductor.
So you cannot have R from one transformer and C from another.
Assuming you have a single stage AC, there should be a two-conductor cable running from the outside unit back to the furnace/air-handler. One of those conductors will connect to Y from the thermostat. The other conductor will connect to the transformer's common side. You should tap into that same conductor for your C conductor.
P.S. Also - that's a DC transformer you have .....
I will see if i can identify those cables. BTW both cables, the one from the handler to the thermostat has 5 or 6 cables in it same from the outside to the air handler.
