On my Quad Copter I have a 5400mAh Li-Po battery (3S 11.1V) and its charger charges at 0.5 C since it takes 2 hours to charge the battery.
That charger has broken down, I have ordered a replacement which will arrive in a few days, however I do have some other chargers that can charge at different rates.
There is one specific charger that only provides 1 Amp which is almost 1/3rd of the usual charge rate those batteries have been witnessing.
All I want to know is whether it is safe to charge a battery with less current than its regular cycle?
At 1 Amp it will take 5.4 hours to charge that battery. It is a balance charger like the existing one so balancing is not an issue. I'm fine with 5.4 hours I just don't want to ruin the battery.
Answer
You can always charge a Li-ion or Li-Po battery at less than its specified rate provided that all the normal charging requirements (CC followed by CV, don't overcharge, don't trickle-charge, don't let the battery get too warm or too cold, etc.) are adhered to.
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