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I have a guitar amp with a fuse on the power socket. It is a 250v 315mA slow blow fuse. My local electronic store only has a 500mA fuse. Can I use that or should I order a 315mA online?

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Order the correct one.

It will work with a 500mA fuse, but you are putting the circuitry protected by the fuse at some risk due to the extra surge current possible. It's quite possible a component will blow rather than the fuse.
In general putting higher rated fuses in is a bad idea, though this is a smallish current and not too different, in extreme cases putting the wrong fuse in can lead to severe damage and possible fire.

So, while the fire or even the severe damage is extremely unlikely in this case, it's worth the wait to order a correctly rated fuse rather than put the wrong one in.

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Can you? Yes. Should you? No.

First, 500mA is 58% more than 315mA. That's a huge increase. Plenty of parts can fry themselves with heat with that much of a difference in current.

Secondly, the original is a slow blow fuse. This means that it is designed to allow more than 315mA, ONLY if it's relatively fast and infrequent. It will wait a few seconds before blowing. A fast blow fuse like the 500mA one you want to use, will take a fraction of a second to blow when it is past it's current limit.

So the question is, how much do you hate that amp that you are willing to fry it?

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You should not use a higher current fuse than what the original one was rated. You should order a 315mA fuse online instead.

The current rating on the fuse will dictate when the fuse will blow. For instance, if the amplifier pulls >315mA with the original fuse, the fuse will blow to protect the circuitry within the amplifier from damage (as well as the power source/supply, in this case, your house and its electrical components!). If you replace it with a 500mA fuse, you can potentially damage the amplifier, your house and its wiring, etc, as the higher-rated fuse will allow the amplifier pull more current than it will be able to handle.

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Specifically, the fuse is normally current-rated to less than the current rating of the power transformer. Other components are either likely to be overated (resistors rated at 500mW or some other nominal value), or to fail suddenly (and not be protected by a fuse), but a power transformer is a big chunk of wire and metalic core, where the cost is proportional to the current rating.

If there is a fault that runs a bit too much current through the power transformer, it probably won't fail. It will just get too hot. Hot enough to melt or burn the case, insulation, paper, wood, cardboard or whatever. Hot over a long period of time, allowing smoldering fires to convert to flame, or allowing smouldering fires to asphyxiate sleeping people. Big thermal mass, so it doesn't cool down quickly when exposed to air.

Will this happen to you? No, probably not. You have to have thousands of fire accidents to get one fatality. Still, bottom line is I wouldn't use the wrong fuse, I'm certain I wouldn't use the wrong fuse in a device that I already know blows fuses, and I'm damn sure I wouldn't lend it to my mother or my little sister after I'd re-rated the fuse.

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