Does the Jackery 500 not show how many watt's are going into the unit, when it is being charged?
How many watt does it say that it is being charged with?
How long does it take before the 15 or 20 amp fuses blow, when you try to charge your Jackery in you vehicle?
The wiring in modern vehicles can sometimes be on the light side of the recommended wire gauge sizes for the max amps that a specific device/outlet is supposed to be able to carry.
This means that the wires themselves get warm, when operated at max capacity.
At the same time, fuses that operate at above 80% of their nominal rating, will also start to get hot.
I have measured car-blade-fuse temperatures, when operating a fuse at about 90-95% of it nominal/fuse value to easily reach 175 - 195 *F ( 80-90*C )
When I used wires that were one to two gauges better than the nominal rating for a wires used in cars, then temperatures of the fuse were lower - because the wires could act as a heat-sinks to the fuse.
But if wires are on the lighter side of the usual/recommended gauge for use in cars, then the fuses are sort of pre-heated, and they are likely to blow at lighter loads, than what they are nominally/stamped to be able to operate at.
With that being said, I have also tested both car-blad-fuses, and other types of fuses used for electronic designs, to typically be able to run for many hours, at amp loads at about 40% over their nominal/stamped amp value.
But the fuses would then get very hot.
I stopped my experiment/measuring when the fuse got above 255*F (125*C) because such temperatures were simply too high for my particular use purposes.
So a separate wire and fuse, going to a high quality charge port for your Jackery 500 , where you also use a higher gauge wire, might very well give you a better chance of having a durable vehicle charge option for your Jackey 500.
Take a look at Blue Sea 12V sockets, for a socket that is designed to be able to last, even when used at the max rated current limits, for hours at a time.
Blue Sea systems also have a good chart for recommende wire gauges, at different amp loads.
https://www.bluesea.com/resources/1437
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But first, look at the watt numbers on the Jackery, when it is being charged.
Take the charge/input watt number, and divide by 12, in order to get the number of amps that your car socket (and fuse) is being loaded at, when the Jackery 500 is being charged.
The Jackery 500 has an MPPT system on the charge input port. MPPT means that the Jackery will internally adjust to what ever is available coming into the charge-input port, , so it will optimize the current pull, to whatever is optimal to reach the fastes charge times that the internal batteries of the Jackery can deal with.
The solar panels, and the AC charge brick, does most likely have their own built-in limiters for what they can survive to deliver (solar panels doesthis by nature, and the AC charge brick will have electronics anyway, in oder to chane AC to DC, so it is inexpensive (and increases safety) to also design a max amp limit for the AC charge brick).
But it is not likely that there is any amp limiting electronics built into the 12V car socket wire.
So how many watts does the Jackey say that is going into the unit, when it is being charged via a car socket?