Final answer:
The statement that a time constant (τ) is the time when an output reaches 63.3% of its final value in response to a step input is true. In electrical circuits, such as RC and inductive circuits, the time constant indicates the speed of the system's response, with smaller constants denoting faster responses.
Step-by-step explanation:
The statement that a time constant (τ) is the measured time when an output response is 0.633 or 63.3% of an input step change is true. The time constant, represented by the Greek letter tau (τ), indicates how quickly a system responds to changes. For example, in an RC (resistor-capacitor) circuit, the time constant is defined by the equation τ = RC, where R is the resistance and C is the capacitance. When τ equals to the product of R and C (t = τ = RC), the voltage across the capacitor has reached approximately 63.2% (≥0.632) of its final value (the saturation point).
This initially derived value continues to be relevant over time, as it characterizes how much the response has progressed towards its steady-state value after a single time constant has passed. The exponential nature of the response means that, with each passing time constant τ, the system progresses an additional 63.2% towards the saturation point from whatever its current value is.
For instance, if we consider an inductive circuit, the inductive time constant τ1 = L/R plays a similar role in determining how quickly current reaches its maximum value after the application of a voltage supply. Smaller time constants indicate faster response to changes, as seen in graphs like Figure 23.42(b) where the current approaches its final value rather quickly.