With regards to whether a 10W solar panel can power a 12V battery, you need to consider a number of things, such as the capacity of the battery, and the amount of voltage in the solar panel.
If you don’t consider the effect of capacity, then to charge a battery with a voltage of 12V, you need a solar panel with a voltage of at least 14V, because the voltage will be unstable during the generation of electricity by the solar panel, and a solar panel with a voltage of 14V or more will be able to provide a reliable voltage for it. So, if the voltage is too small, you cannot use a 10W solar panel to charge a 12V battery.
If the voltage of the solar panel is not taken into account, when the 10W solar panel is charging a 12V battery, there may be a problem with the time, which is too long, and it is also not recommended to use it to charge a 12V battery.
For example, for a 45Ah 12V battery using this panel may take 54 (45 ÷ 10 × 12 ≈ 54h) hours, which is obviously too long and not suitable for charging with a 10W solar panel. Whereas a 5Ah 12V battery may only take 6 hours, it is clear that for a small 12V battery, 10W is sufficient. However, this charging time is also related to the weather, in sunny weather, the solar panel is more effective in charging the battery, but in cloudy weather, the solar panel can generate electricity, but the power generation is smaller, and the time may be longer.
You need to go for picking up a proper solar charge controller, which will save your battery from overcharging or over-discharging during the charging process, ensure the performance of your battery and make your battery last longer.
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