If you apply a direct current source to a capacitor, it will pass DC just fine. (The voltage will increase until the cap explodes, of course...) If you apply DC voltage to a capacitor it is not at all blocked at first. Eventually, the capacitor gets charged and puts out its ow n DC. At that point no current flows through it.
The important thing is to understand that it is happening. Capacitors do pass current, whether DC or AC. DC current does not pass through because there is no conducting path from one side of the capacitor to the other. AC current "passes through" in a different sense than conduction through the device.
If you apply DC voltage to a capacitor it is not at all blocked at first. Eventually, the capacitor gets charged and puts out its ow n DC. At that point no current flows through it. I think it would help to understand how a capacitor blocks DC (direct current) while allowing AC (alternating current).
DC current does not pass through because there is no conducting path from one side of the capacitor to the other. AC current "passes through" in a different sense than conduction through the device. As much charge enters one side as leaves the other. But this cannot be maintained forever; eventually one side will run out of electrons.
If a battery is connected to a capacitor, it will allows no direct current (DC) to flow through. If a not charged capacitor is connected across the terminals of a battery, a transient current flows as the capacitor plates charge up. Current flows from the battery terminals to the capacitor plates.
If a not charged capacitor is connected across the terminals of a battery, a transient current flows as the capacitor plates charge up. Current flows from the battery terminals to the capacitor plates. The positive battery terminal, attracts electrons from the upper capacitor plate. The plate is positively charged.