I have an old oscilloscope which doesn't work. I tried swapping the 3.15A/250VAC fuse with a 4A/250VAC fuse. The fuse immediately blew. My questions are: Did the fuse blow because it was the wrong fuse? Or did it blow because there's likely something else wrong with the oscilloscope? Must the fuse be exactly as specified? Thank you.
First, replacing a fuse with one of a higher current rating is a bad idea. In this case, assuming the two fuses were the same type (fast or slow blow), then there is definitely something wrong with your scope. Since the scope is not meant to exceed 3.15 A, but actually exceeded 4 A, there is clearly something wrong. By making it take more current before the power was shut off, you may have even damaged it further.
This is all assuming the two fuses were of the same type. If the original was a slow blow, and the new a fast blow, then what you observed could still happen in normal operation. Look at the old and new fuses carefully. This isn't universal, but usually a fast blow fuse is just the melting link suspended between the ends. A slow blow usually has the melting wire wrapped around a ceramic rod.
If the original was fast blow and you replaced it with a slow blow, then there is really something wrong with the scope.
It is also possible that you have different types of fuse between the 3.15 A and the 4A. Fuse comes in two types: Slow-blow and regular. Slow blow fuses are used when there can be a short-term current surge in the system, like when you power on your oscilloscope. If the old 3.15A is a slow-blow and you put in a 4A regular, it will blow right when you turn it on, which is what you are seeing. I'd suggest looking at the 3.15A to see if it's a slow-blow kind or if it's a regular. Then you need to match the 4A to it. I'd bet that it's a slow-blow.
By changing the fuse to a higher current, you are changing the power which the oscilloscope can draw from the wall. The power is $$ P = IV $$ for current \$I\$, voltage \$V\$. So by moving from a 3A to a 4A fuse you are increasing the power available inside the scope by about 30%.
You're unlikely to start a fire by switching to a 4A fuse, but I wouldn't go any higher without debugging the actual problem.
Just a comment.
If this is a T3 fuse, (small, glass or ceramic tube, measuring 20mm length x 5mm diameter) you are likely mis-reading the etched info on the silver end-cap.
Are reading is T3.15A250V, yes? The period/dot may be a separator that indicates you have a T3 fuse, with a 15A, 250V rating. (I'm looking at a ceramic one I just removed from a power supply right now as I type this ... it's definitely a 15A fuse ... and is marked as such on the fuse holder in the power supply as well.) Amps did not used to be marked with periods, per the old standard,
So that could explain why you are instantly blowing a 4A fuse. You probably need to draw somewhere near 5-10 Amps through that part of your device (likely the electron gun of the CRT on the oscilloscope). Beware though - we haven't eliminated the possibility of a fault. Something blew the original fuse ... be physical weakening due to age / impact or a true fault.
Long story short, read your manual (or Google for it) and verify what you need ... especially if you picked up the device second-hand. You never know what the previous owner installed correctly or incorrectly. Trust, but verify. ;>
PS: T shapes come in multiple sizes (eg: 1/4"d x 1-1/4"l) and in both glass (with metal link) and ceramic. In something like an oscilloscope (or anything with a CRT) I wouldn't be surprised to see a ceramic fuse to prevent the possibility of arcing in a very high current-flow failure.
Edited to correct something ... there are 3.15 Amp fuses are marked in A and not mAh ... something I had not previously seen. Thanks to Sam, for pointing that out.