How can a transistor amplify current in a circuit?

My answer (March 1, 2021) to SE EE question How can a transistor amplify current in a circuit?

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This is one of my favorite topics for discussion that makes me a little extreme in my speech... but I cannot put up with such a simple, clear and obvious phenomenon being explained in vague ways... That is why, when I saw the answers and comments under the question, I wrote my answer in one breath...

My answer

In fact, OP has understood the naked truth about the transistor "amplifier"... that it is not an amplifier at all... on the contrary, it is an "attenuator". At this stage, OP does not need detailed explanations; he needs confirmation of his guesses.

It is considered the transistor is an active element used to build amplifiers... but IMHO this is not true. The transistor is not active but passive element; the only thing that it can do is to dissipate power. So, the transistor is not amplifying but attenuating element. It is just a "resistor" (non-linear, electrically controlled but still a resistor) that decreases the current.

The true amplification is impossible; so there are no real amplifiers. The so-called "amplification" is just an illusion, a clever trick... and the "amplifier" is just a "magic box" where we see higher output power... but this is not the amplified small input power. This is else's power... of the supply source.

In analog electronics, we implement such an "amplification" in the possibly most paradoxical, absurd and silly way - to obtain output power higher than the input one, we get a big power source and then throw away a part of it (from zero up to the whole power). In comparison, in energetics, they can not afford to do it.

I use this approach in classes with my students to clarify such vague definitions of amplifier as "electronic circuit that uses electric power from a power supply to increase the amplitude of a signal applied to its input terminals" (Wikipedia). For example, here is a seminar in 2004, in which we discussed the philosophy of the transistor "amplifier". Another Wikibooks story from 2008 describes how my students studied this phenomenon in the lab in order to reinvent the BJT current mirror.

In 2013, I asked a similar ResearchGate question which provoked a heated discussion. I hope it will be useful to you.

My comments

1. It is accepted that "amplifier" means "power amplifier". So the "voltage amplifier" and "current amplifier" must also be "power amplifiers".
2. It seems so ... although your question makes me think ... Obviously, the requirement for power amplification is important ... because when we have power we can convert it into whatever voltage or current we want ...
3. Wikipedia: "An amplifier is a circuit that has a power gain greater than one."
4. That is why I have said "the true amplification is impossible; so there are no real amplifiers" and "the so-called 'amplification' is just a trick"...
5. The "trick" explains how such a circuit "performs energy conversion" and what it actually does. It is a "silly trick" because the excess power is thrown out (in contrast to switching amplifiers)... but still all analog electronics is based on it. My goal is to explain the phenomenon by showing its manifestations around us in various sometimes fun and even comic situations... but not by sterile definitions... because this is the way we understand phenomena. "Explaining" through definitions leads to asking thousands of questions here... and we do the work of those who have not done well...
6. "Converter" is another term that is frequently used in analog electronics in such a figurative way. In many cases, we do not convert anything but only assume (change) one quantity as input and another as output. A typical example is the simple "voltage-to-current converter" where there are both voltage and current... and we change the voltage as input and take (measure) the current as output. But we can do the opposite, indeed, in a more sophisticated way - adjust the current equal to some (input) value by changing the voltage. As a result, we obtain a "current-to-voltage converter"...
7. So all these "converters" are not converters in the literal sense of the word ... Or, if we still want to call them "converters", we should clarify that they are something like "informational converters".
8. They are figuratively called "converters" but actually they do not convert anything... everything is the same...
9. Yes, we simply say it in that way maybe to save the long explanation. But the more important thing is to understand what is happening in this arrangement. I would explain it this way: A change in temperature leads to a change in resistance, which in turn leads to a change in current according to Ohm's law. In short, we can consider this arrangement as two cascaded "temperature-to-resistance" and "resistance-to-current" converters. Unfortunately, the latter is nonlinear; that is why, we prefer to use "resistance-to-voltage" converter (ie, we supply the thermistor with constant current).
10. Instead "converter", we can say "functional block" with an input and a related output. In this way, we will focus on the fact that some (output) electrical quantity depends on another (input) quantity. But I have nothing against the word "converter" if only we clarify what it is. By the way, I also use "voltage-to-voltage converter" = "voltage-to-current converter" + "current-to-voltage converter" (potentiometer, inverting amplifier...)