Signal Generator and AC power supply

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What is a difference between sine Signal Generator and AC power supply?
 
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A mains AC power supply is a fixed-frequency 50Hz or 60Hz (depending on country) sine wave signal of high power and fixed voltage. A sine signal generator is variable frequency, low power, variable voltage.
 
the AC power outlet can likely deliver a lot more voltage (120 V r.m.s.) and a lot more current (perhaps 15 A or 20 A) than any signal generator you can buy. and, hence, a lot more power.

the AC power outlet will not have adjustable voltage or frequency. and the signal generator might have a cleaner sine wave.