When is the current through a charging capacitor at its maximum?

The current through a charging capacitor reaches its maximum when the voltage is changing the fastest. This occurs at the initial stages of charging when the voltage across the capacitor is still relatively low. During this time, the capacitor begins to accumulate charge, and the rate of change of voltage is maximized, resulting in the highest current flow from the power source into the capacitor.

As the capacitor charges, the voltage across it increases, but the rate of this increase slows down as it approaches the maximum voltage (the supply voltage). Eventually, when the capacitor is fully charged, the voltage stabilizes, and the current drops to zero. Therefore, the relationship between current and voltage change is key: maximum current correlates with maximum rate of voltage change, not with maximum voltage itself or zero voltage.