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I am currently introducing some basic electrical concepts to some people within the Study Group whose understanding is very limited and have produced the attached- posting in case others find it useful as well.
The current is not flowing because the filament of the bulb is broken, this opens the circuit, just as the switch does when it is turned off.
The current is zero because the resistance of the broken filament is very large (it tends to infinity for practical purposes) and the current is then I = V/R = V/inf = 0.