What will happen if we give voltage to a transistor (BJT) across emitter and collector without connecting the base? Will it conduct current?
And what will happen to the barrier potential which is across emitter-base and base-collector?
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There will be some small current from collector to emitter due to leakage.
First of all, linear models of a BJT (like hybrid pi model) often include a resistance in parallel with the collector to emitter path.
Second there is some small leakage from collector to base. That leakage will then be amplified by the base (as any other base current would be) resulting in additional collector to emitter current.