An uncharged 1.0-μF capacitor is connected in series with a resistor, an ideal battery, and an open switch. What is the voltage across the capacitor after closing the switch?

Just after closing the switch, zero; when the capacitor is fully charged, the voltage is equal to the voltage of the battery

Explanation:

A capacitor is a device able to store charge. It generally consists of two parallel metallic plates separated by an insulator (usually air), so that charge cannot pass through the gap. Therefore, when the capacitor is connected to a battery and a current starts circulating through the circuit, negative charge accumulates on one plate of the capacitor, while the other plate acquire an equal and opposite positive charge.

This process continues until the capacitor is fully charged, which means when no more charge can be accumulated on the capacitor.

At the beginning, when the capacitor is uncharged, there is no electric field between the plates of the capacitor, so the voltage across the capacitor is zero.

Later, as the capacitor charges, the electric field between the plates increases; when the capacitor becomes fully charged, the voltage across the capacitor is exactly equal to the voltage of the battery.