Problem calculating fuses

I am calculating a fuse and I'm having a bit of trouble. I have a 12v 2A power supply that I want to protect, so my first thought was to place a fast 250v 2.5A fuse in series so it should blow if a short circuit or overload happens. The thing is that testing it with a current limited power supply of 12V/3A and shorting it the fuse does not blow at all, it keeps working happily.

Doing some tests using each time smaller fuses I got it to blow with a 250v 0.1A, extremely lower than what it should be, anything higher does not blow at all.

According to Joules law what should matter is only amperage, as the fuse is in series with the circuit and the resistance is constant (p=I2*R).

If I calculate the total power disipation it's 36w (12v*3A) and if I calculate the fuse as if it dissipated power it should support 25w, so I tested a 0.2A fuse and it works as it should support 50w.

Thinking that there was something wrong with my set-up and calculations I used another power supply and created an extremely simple circuit with a 5ohm 1/2w resistor and a 250v/0.2A fuse. According to this setup the circuit should be powered with 1v to get to the maximum supported current, it should not blow but be very near to it.

Ok, I powered and everything was ok, it drew 200mA from the power supply and the fuse was ok. So, I wanted to blow it, I pushed up the voltage to 1.5v, that started to drew 300mA, the fuse didn't even noticed it... I pushed up the voltage more until it the resistor started to smoke, it was at 2~2.2v, 0.45A, nearly 1w, more than twice the fuse specs... The circuit is still running near me at 1.5v/300ma like a boss after 4 hours...

So, where am I wrong? What's happening here? Why the fuse is ignoring amperage and seems to be blowing up by the power dissipated by the circuit and not by amperage?

EDIT: I have extended the test, a 2.5Ohm resistor 1w, I got the fuse up to 1A and obviously the resistor started to smoke but the fuse still works... I reduced the voltage to 1.5v, the max supported by the resistor and the fuse is conducting 0.6A like a boss...

EDIT2: Here is a picture of the final circuit, which should blow the fuse but runs smooth as butter...

EDIT3: It was running 3 hours at 595mA with no change, I checked everything with an external multimeter and all was ok, also, I tested it with two power supplies...

Searching I have found a statement at wikipedia that says:

Medium-voltage fuses rated for a few thousand volts are never used on low voltage circuits, because of their cost and because they cannot properly clear the circuit when operating at very low voltages.

So, it seems that a 250v fuse cannot be used with low voltages like I'm doing, but I can't find why...

On my final circuit I'm going to use a resettable fuse rated 16v 3A, that will for sure remove any trouble, but I really would like to know why this happens.

• which side of the power supply is the fuse on? ... input or output? – jsotola Sep 21 '19 at 2:58
• On the input, else the fuse would do nothing if the short happens in the power supply itself. But just forget the initial part, check the last test I did, I have added the schematic. It's holding 0.6A without any problem... – Gusman Sep 21 '19 at 4:08
• how are you measuring the voltage? ... are you using slo-blo fuses? – jsotola Sep 21 '19 at 4:52
• The power supply has a voltmeter and ampmeter integrated and I also checked the voltage at the power supply output with an external voltmeter and it matches the values. And no, this are fast fuses as I wanted fast protection. Even if this were slow fuses, 4 hours with twice the specified amps should be more than enough I think... not to say it's been running 1.5 hours with three times the specs (600mA)... – Gusman Sep 21 '19 at 4:54
• The thing is that I see the total current in the circuit... it's drawing 600mA from the power supply (595.7 mA) so there's no error possibility about that – Gusman Sep 21 '19 at 5:01