hl_world said:
& current is that between points B[/color] & D[/color] there is a 2v supply. This will cause the current to flow through the 40Ω resistor a lot more than the 2kΩ.
That would be true if there were only 40Ω in parallel with the 2kΩ. However, it is an LED+40Ω series combination in parallel with the 2kΩ. We don't know what the effective resistance of the LED+40Ω is, so we can't say that more current flows through that path.
Also, thinking of this as a voltage divider: the resistance of the lower section must be less than 2kΩ, due to the LED+40Ω that is in parallel with the 2kΩ resistor. That would mean V
BD is less than 2V.
Another observation: if any appreciable current does flow through the diode, it would have close to 2V, which means close to 2V between C and D. But there is also 2V (or close to it) between B and D. So therefore a very small voltage is between B and C. Just how small we don't really know, but if the circuit were actually built one could measure V
BC, and divide it by 40Ω to get the actual current in that path.
One cannot ignore the effect of the LED on the LED+40Ω branch of the circuit.
Hope that helps clear things up

. If not, keep posting. You have a pretty good grasp of the basics, so that helps a lot in composing answers to your questions.