Final answer:
The voltage across the plates of a charged capacitor opposes the electromotive force (emf) of the battery. It grows from zero as the capacitor charges, eventually matching the battery voltage, which reduces the current flow to zero.
Step-by-step explanation:
In a charged capacitor, the voltage across the plates opposes the electromotive force (emf) of the charging source, such as a battery. This voltage, denoted as Vc = Q/C where Q is the charge stored on each plate and C is the capacitance, acts counter to the applied voltage and grows from zero to the maximum emf when the capacitor is fully charged.
As the voltage on the capacitor increases, it creates an opposing force that reduces the current flow—eventually to zero, at which point there is no longer a voltage drop across the resistor (IR drop), and the voltage on the capacitor equals the battery emf.
This opposition to the flow of charge is also due to the repulsion of like charges that accumulate on the plates during the charging process. Kirchhoff's second rule, which states that the sum of potential changes around a closed loop must be zero, further explains this relationship.