Robyee wrote:
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My UPS is definitely 'dead' and I'm wondering if i can use the Mac Mini without buying another one
That totally depends on your usage.
Generally, computers, especially with SSDs, are much more robust in terms of handling power outages. While there is no guarantee that something bad will happen, the odds of it are pretty small.
However, if you are doing things on your computer that you cannot afford any loss of work in progress items, then you will most likely want to get a new UPS. This is especially true if you are doing work on the computer for work or a business, in which case a UPS could be cheap insurance against lost dollars. Example might be you have been working on a document for the past hour or two and the power drops out. All that work could be lost.
In terms of surges, computers in general must be designed to certain UL (or the regulatory entity in your country) guidelines for certification. However, they generally cover maybe 90-95% of those types of occurrences so you may want to consider additional surge protection depending on your electrical supplier.