Describe the transient response of an RC circuit to a step input.

When a step voltage is applied to an RC circuit, the capacitor voltage follows an exponential curve: Vc(t) = Vs(1 - e^(-t/RC)) for charging, where RC is the time constant. The current starts at maximum (Vs/R) and decays exponentially: I(t) = (Vs/R)e^(-t/RC). The transient lasts approximately 5 time constants, after which the circuit reaches steady state. This response is fundamental to timing circuits, filters, and digital signal processing.