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Emitter current is the sum of collector current & base current , hence the largest. Base current is the smallest.
The active region of a transistor is when the transistor has sufficient base current to turn the transistor on and for a larger current to flow from emitter to collector. This is the region where the transistor is on and fully operating.
In the switching transistor the output current is controlled by the (current) and this is also called current controlled current device (CCCD). But in ordinary switch we controlled output current physically...
in a properly biased transistor, collector and emitter current also decrease
The difference between a Transistor and a Resistor is that a transistor is designed to amplify the electrical current, whereas a Resistor is designed to reduce the electrical current.
emitter current
The saying "at what current is transistor biased" means to ask the current through the transistor when there is no signal present. Typically, a transistor is biased at the center of its linear region, so as to minimize distortion. This, of course, depends on whether or not the transistor is AC or DC coupled, and where the clipping points might be.
hf
Transistor increase the strength of a weak signal from the base
The total current in a transistor is the emitter current, which is the sum of the collector current and the base current. The ratio of collector current over base current, in linear mode, is beta-DC, or hFe. However, in order for linear mode to be true, the ratings of the transistor must not be exceeded, and the collector current must not be limited by the circuit. Note also that hFe is temperature dependent, and is expressed in the data sheet as a minimum, not an absolute value - it can vary from transistor to transistor.
The cutoff region is when the transistor doesn't have sufficient base current to drive a larger current from emitter to collector. Therefore, the transistor does not turn on and stays shut off.
Base of transistor is made thin just to get Collector current equal to Emitter current.