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If we take as an example, a power supply such as one found in a PC, which takes 110/220v and steps it down to 3.3v/5v/12v. We can usually draw 30 amps from the 12v line with no problems (360 watts of power). But the power supply is connected to an extension cable with a 13 amp fuse.

Therefore, it must be the case that the current on the 110/220v side is not nearly as much as the current on the 12v side.

But how is that possible? If current is a measure of charged particles moving across a point, how can that change by changing the voltage? Is it the case that the higher voltage particles have more "speed" or "energy" so that one of the moving faster can push 3 of the lower voltage particles?

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In a transformer, the primary and secondary coils are disconnected. So the currents under different voltages are not connected by wire. The connection is through the magnetic field in the transformer. This connection essentially transfers power between the coils. Power (simplified) is a product of voltage and current. So if you double the voltage and the power is the same, the current drops in half.

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  • $\begingroup$ Does the same principle apply in switching power supplies that don't have a transformer? $\endgroup$ Commented Aug 3, 2017 at 21:56
  • $\begingroup$ Yes, it does, because swotching power supplies do have transformars. The difference there is that switching power supplies work at a much higher frequency than 50 or 60 Hz of regular AC. The higher frequency allows the transformer to be much much smaller. So instead of being a main heavy component on the chassis, the transformer becomes more like a coil on the circuit board. Some of them (called SME Inductirs) can be found on some computer motherboards and sometimes emit a high pitch sound. Of course another difference is switching the current abruptly, but this is irrelevant to the question. $\endgroup$
    – safesphere
    Commented Aug 4, 2017 at 3:50
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Power = V x I, that is power is equal to the voltage times the current. Neglecting losses for the moment, the power going into a transformer is the same as the power coming out. If the output power is 12V x 30A, we get 360 watts. So the input power must be about the same and actually slightly larger to account for losses. With 110V input the input current would be about 3.3A.

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