In RC circuits, the voltage across the resistor leads the voltage across the capacitor by 90 degrees due to the relationship between current and voltage, where voltage is proportional to the integral of current. Conversely, in LC circuits, the voltage across the inductor lags the current by 90 degrees because voltage is proportional to the derivative of the current. This phase difference arises from the fundamental properties of capacitors and inductors in response to alternating current. Understanding these relationships helps clarify the behavior of AC circuits without solely relying on mathematical equations. The discussion emphasizes the importance of recognizing how voltage and current interact in different circuit components.