Circuit builder for beginner showing the light of LEDs and electical flow
The general term is circuit simulator. This one is most likely what you are looking for:

http://www.falstad.com/circuit/

Though there's no differentiation between design mode and debug mode, it still is quite powerful, since it simulates on-the-fly as you draw.



As you progress, this will become insufficient and you will have to convert to something like LTSpice.