Batteries create a potential difference by having unequal electron distribution, leading to instability that drives electrons through the circuit. This process charges the capacitor plates, with one plate becoming negatively charged as electrons accumulate, while the other plate becomes positively charged. As the capacitor charges, the voltage across its plates increases until it equals the battery voltage, at which point the current ceases. The discussion clarifies that there is a current during the charging process, which falls exponentially until the capacitor is fully charged. Ultimately, the relationship between the battery and capacitor is characterized by the balance of potential differences.