Resistance, capacitance, and time are intricately related through the time constant formula τ = RC, which defines how quickly a capacitor charges in an RC circuit. The time constant indicates that after five time constants, the circuit reaches a steady state where the capacitor is fully charged. As time progresses, the voltage across the capacitor increases exponentially, described by the equation Vc(t) = Vf(1 - e^(-t/τ)). In this context, the voltage across the resistor decreases as the capacitor charges. Understanding these relationships is essential for analyzing circuit behavior in electrical engineering.