Take a circuit comprised of resistors, a single capacitor, and a single step response voltage source. Then:
Every single voltage and current in the circuit, except at the voltage source, will have a *e^(-t/tau) dependency.
Where tau, the time constant, is the capacitance times equivalent resistance seen by the capacitor.
Why are 1 and 2 true? I understand why it is true for a resistor connected in series with a capacitor but not why this can be generalized, especially since not every RC circuit can be simplified into a resistor in series with a capacitor.