Active region:
In this region collector diode is reverse biased and emitter diode is forward biased. Consider first that emitter current is zero. Then collector current is small and equals reverse saturation current ICO of collector junction considered as a diode.
If forward current IB is increased, then the fraction of IE that is αdcIE will reach the collector. In active region, the collector current is independent of collector voltage and depends only on the emitter current. Because adc is, below one but almost equal to unity, the magnitude of the collector current is a bit less that of emitter current. The collector current is constant and work as a current source.
The collector current increases slightly with voltage. This is because of early effect. At higher voltage collector gathers in a few more electrons. This reduces base current. The difference is so small, that it is neglected usually. If the collector voltage is increased, then the space charge width increases; this decreased effective base width. Then there is less chance for the recombination within the base region.
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