How do transistors amplify signals?

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d logician
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i have no idea how transistors amplify ...how can the output gain be greater than the input gain ? ...efficiency is output/input which can never be greater than one, right?
 
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sorry how can output be greater than input ...not output gain greater than input gain
 
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Do you understand how a relay works? It uses low voltage and low current to switch a higher voltage and higher current. Transistors are similar.

In the case of transistors, a small input current controls the amount of current drawn from a power supply to create a much larger replica of itself at the output. Efficiency in the case of amplifiers is not the output signal divided by the input signal but the output power divided by the total input power from the power supply. The power supply always supplies more power than is available at the output so the efficiency is still always less than one.