Electronic – What’s the real inrush current in the AC/DC rectifier

A 50VA transformer will take about 0.21 Amps when correctly loaded (VA / Input voltage)

So a fuse of about 1.5 x the input is suggested and should be Anti Surge (Usually marked T or TT - T stands for "träge" which is german for Lazy or slow) - so 315mA A/S or 400mA A/S

If your fuses are vaporized and cover insides with remains of the wire - This indicates a major short...

What type of transformer are you using - is it a toroidal - if so have you got a shorted turn (if you mount a toroidal transformer incorrectly you can add an extra winding which is shorted out - this is creates by mounting the transformer with a conductive clamp which is bolted down in the middle - if you are using a toroidal - try removing the clamp...)

It is possible that you have a faulty diode in your bridge - I have seen diodes that measure OK when tested with a meter, but when either loaded, or subjected to a higher voltage, break down and become shorts, or leak - the easiest way to prove is to replace ALL the diodes, as I have found if one is faulty, it usually subjects others in the bridge to stress, which may make them more likely fail, and for the cost of 4 diodes of 1N400X or 1N540X - I usually use 1N4007 or 1N5408...

Either can work correctly if designed properly. If you have a dumb rectifier supply feeding a 7805, then all the rectifier part needs to do is guarantee the minimum input voltage to the 7805 is met.

The problem is that such a power supply only charges up the input cap at the line cycle peaks, then the 7805 will drain it between the peaks. This means the cap needs to be big enough to still supply the minimum 7805 input voltage at the worst case current drain for the maximum time between the peaks.

The advantage of a full wave rectifier is that both the positive and negative peaks are used. This means the cap is charged up twice as often. Since the maximum time since the last peak is less, the cap can be less to support the same maximum current draw. The downside of a full wave rectifier is that it takes 4 diodes instead of 1, and one more diode drop of voltage is lost. Diodes are cheap and small, so most of the time a full wave rectifier makes more sense. Another way to make a full wave rectifier is with a center tapped transformer secondary. The center is connected to ground and there is one diode from each end to the raw positive supply. This full wave rectifies with only one diode drop in the path, but requires a heavier and more expensive transformer.

A advantage of a half wave rectifier is that one side of the AC input can be directly connected to the same ground as the DC output. That doesn't matter when the AC input is a transformer secondary, but it can be a issue if the AC is already ground-referenced.