Mixing different batteries, whether in parallel or in series, is a bad idea. Even enough of the same type of battery wired together is a bad idea.
Batteries are complicated electro-chemical devices. They vary quite a bit with temperature, age, state of charge, discharge rate, and what your dog had for breakfast. There is enough variation between "identical" batteries coming off the same assembly line that you have to be careful in combining them. With different batteries, the answer is simply "don't do that".
With primary cells, there is more forgiveness since they are used once until dead, and therefore future ability to be rechargeable and hold a predictable amount of energy is irrelevant. As such, it is allowable to let primary cells possibly suffer some damage as you try to get the last bit of energy from them. However, if you go too far, they could rupture and cause physical damage to whatever equipment they are contained in.
Rechargeable cells have to be treated much more carefully. Even just putting 4 cells, for example, in series is not so simple. One cell will inevitably have lower capacity than the others. This cell could be discharged so far as to cause damage, even when the stack voltage looks OK (the average cell voltage is above the damage limit).
Charging has the same issue. The lowest capacity cell can be overcharged and damaged before the highest capacity cell is really full.
Properly designed systems with multiple rechargeable cells in series will have monitoring of individual cells, and usually some kind of "charge balancing" circuitry. This shunts some of the charge current around the higher voltage cells to let the lower voltage cells catch up. On discharge, the current is stopped as soon as the lowest cell gets to the point where continuing would cause damage.
To make things more tricky, there isn't a hard line between damage and no damage. There are gray areas where deeper discharge or higher charge starts to decrease lifetime of the cell. That lifetime is itself really a probability.
It gets complicated, and proper multi-cell battery management is a deep topic and will get significant design attention in real professional systems intended for a long life.
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The kanine nurishment dependency can have particularly tricky influence on performance, so has attracted much research. According to a study commissioned by the Project for Object Oriented Paradigms and performed at the Boise Institute for Technical Excellence, this complex relationship can be distilled down to one simple to understand graph:
Combining batteries which are not the same type and/or model and/or chemistry is always a VERY bad idea.
Combining SLA and VRLA is a NO GO.
You only would want to do this with batteries of the same type, model, capacitance and age. Combining any other way is asking for trouble.
Best Answer
Since you are talking about connecting to a lead-acid battery it's pretty clear that there are no high frequency signals involved, so the inductance of the cable (and the skin effect) are not relevant in this case.
For low frequencies, larger diameter cables will provide less resistance to current flow so they are generally preferred. Electrically, it is OK to connect heavier cables to smaller cables. However there is some risk here and the practice may be prohibited by local electrical codes. For example, you connect a cable and plug designed for 30A to another wire that is rated for 15A. You know the limitation of the entire circuit is 15A, but someone else comes along, sees the 30A plug, and tries to draw 25A through the circuit. That would be a fire hazard.