I had to charge my car battery two days ago. I used another car's battery to do so.
I accidentally reversed polarities (+ with -) and vice verse. There were very strong sparks.
I was trying to understand the reason behind it mathematically, but I couldn't find any
reason behind this behavior online.
If you short out one battery you get sparks because of the high discharge current actually melts metal which flies-off from where the short is made/enacted.
If you wire two batteries in series and short the combined series battery out you'll get sparks, maybe even bigger ones.
Now, think about what you did - you put two batteries in series and then created a short. I know you think you put two batteries in parallel but draw out the circuit and you'll recognize that wiring one one wrong way round (in parallel) is like shorting two in series out.
If you wired two batteries in series but they were "opposing" (+ to + and - to -) you'd just get a small current flow as they equalized in voltage - this is called putting them in parallel BUT you can also see that they are in series with a short added.
