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Why does the transformer hum
Why does especially the toroidal transformer hum, sometimes hard? The iron core is very efficient and the magnetic flux is high, very near magnetic saturation of the core. This gives very little room for "extra" flux which DC can cause. DC on AC mains is simply unsymmetrical waveform of the sinus wave. What happens if you have a hair drier with half speed? This is accomplished with a diode and halfway rectification, causing the positive peak voltage become lower than the negative. This creates a small DC level which some apparatus don't like, especially toroids. An another reason for DC on the mains is switching transients in large networks.
The DC trap makes sure that no DC slips through. The primary winding is AC coupled with help from two big electrolytic capacitors. The inrush current will go through the diodes when the capacitors have been charged over 1 or 3 volts and the normal current will only go through the capacitors.