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Bipolar transistors (bipolar junction transistors: BJTs) can control the collector current via the current applied to the base. Typically, the collector current is the base current times the DC current gain (hFE)*. It is this gain that allows bipolar transistors to be used as amplifiers. Bipolar transistors are also utilized as switches using their characteristics in the saturation and cut-off regions.
*hFE varies with the collector-emitter voltage, which depends on external circuitry.
For a description of hFE, also see the FAQ entry, “What is the relationship between the base-emitter and the collector-emitter voltages of a bipolar transistor?”.