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Comment by periblepsis on What happens in a circuit when load current is very small?

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@Wanda Ebers-Moll predicts this. Assume Vce=0 and a Shockley current based on the BE junction as I. If BF=200 and BR=3, expect IB=(1/3+1/200)*I, IC=-I/3, and IE=-I/200. (The minus means it exits the terminal.) From the circuit, the base current is about 2.43 mA. So the collector current will be -2.394 mA and the emitter current about -36 uA. That won't support the emitter voltage via the 10k resistor to ground, so the BJT slightly adjusts its emitter voltage. Just enough so that the emitter current can increase to about -500 uA.

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