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Typical "wall-wart" switching power adapters are often rated for ~110-240V 50-60Hz AC input and output low-voltage DC. For this question let's assume the output voltage is 5V DC.

Internally, the adapters pass the AC input through a rectifier to produce pseudo-DC, and ripple is reduced with one or more reservoir capacitors. The now-smoothed DC is then sent through other electronics (e.g. a transformer, a switching element, regulator, etc.) to produce the DC output voltage.

Can these adapters also be powered by a DC input?

My naive assumption is "yes", since the AC input is rectified to pseudo-DC and the internal components operate on the pseudo-DC. This seems to be supported by this page, which states in part

The reason for the lower frequency limit being imposed is owing to the smoothing capacitor not being able to hold enough charge between cycles. The lower the frequency the higher the ripple, the higher the ripple the hotter the cap will run. The upper limit is due to the above mentioned input filters starting to filter out the mains frequency and, as they would now be absorbing energy, would run warm.

Powering a SMPS from DC eliminates both the above problems. The capacitor is no longer required to hold a charge between cycles as the DC will maintain a constant input voltage and the filters would merely prevent any unwanted spurious generated by the SMPS from reaching the incoming supply.

The only concerns when operating a SMPS from DC is the incoming voltage range that ensures correct operation. The lower DC limit is the lower AC limit multiplied by 1.414 e.g. 85VAC would mean 120VDC lower limit. The upper limit of 240VAC equates to 340VDC, 265VAC being 375VDC, levels not usually found.

Does this seem reasonable?

Are there any risks, either to a person or to the adapter itself, that might arise if testing such a setup (other than the typical risks of working with mains-level voltages)? While one risks failure by using a higher-than-rated input voltage, should one expect issues if using a lower-than-expected voltage? For example, while connecting an adapter to a 12V DC input might cause it to not work, is it possible to damage the adapter?

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Powering such a device from DC is perfectly fine, in fact usually the input is rated both for AC and DC. You just need to be very careful about the input voltage though: when you rate an AC input you usually give the maximum peak to peak voltage amplitude, but when you rectify it there is that 1.414 factor, also known as \$\sqrt{2}\$, that must be taken in account.

So, no risks for the user or the adapter. If you exceed the maximum input voltages some capacitors are going to explode (at least), if you use a lower input voltage the adapter won't work properly and might heat up due to undervoltage protections.

I'm guessing you want to power your laptop with your car battery: that is possible but not just hooking the laptop adapter to the battery.

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    \$\begingroup\$ I already answered this: the adapter won't work but won't even be damaged. It might work but it seems very, very unlikely to me. \$\endgroup\$ Commented Jun 10, 2014 at 12:53
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    \$\begingroup\$ I'll disagree slightly with Vladimir here and say that you should give it at least \$\sqrt 2 \times V_{MIN}\$. Using less could conceivably cause overheating since undervoltage protection is typically pretty crude. \$\endgroup\$ Commented Jun 10, 2014 at 12:55
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    \$\begingroup\$ I was also thinking: may it be that the adapter would work but would request much more current than normal with a full loaded output? That makes sense to me... \$\endgroup\$ Commented Jun 10, 2014 at 12:58
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    \$\begingroup\$ @SpehroPefhany I edited the answer correcting that part, I did not think of undervoltage protections. \$\endgroup\$ Commented Jun 10, 2014 at 12:59
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    \$\begingroup\$ Can circuitry for power factor correction always be assumed to behave nicely when given a DC voltage? \$\endgroup\$
    – supercat
    Commented Aug 27, 2014 at 17:14
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This will work fine until you have a short on the AC side upon which the poor AC rated fuse will see a DC arc. If you’re lucky, it will manage to break the current and everything is fine. If not, the arc will persist until you have a fire or enough material has evaporated away for it to self-extinguish.

Some SMPS vendors do rate their supplies for DC, mostly industrial stuff. Design would be identical except for fuse/input protection side.

Here is a good example of an AC versus DC arc. Same voltage, same current. https://youtu.be/Zez2r1RPpWY?si=zAE7TJ3XKcb4gqD7

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