The time constant in a transmission system is the time necessary for the response curve to reach what percentage of its final value?

In a first-order transmission system, the concept of the time constant is integral to understanding how quickly the system responds to changes. The time constant is specifically defined as the amount of time required for the response curve to reach approximately 63.2% of its final value. This value comes from the natural logarithm function, as it represents the response of the system to a step change in input.

The time constant plays a crucial role in various engineering applications, particularly in control systems, because it helps in predicting how fast a system will react to inputs. When the time constant is known, engineers can design systems that behave in predictable manners, ensuring stability and responsiveness in processes.

Thus, the correct choice highlights the unique characteristic of the time constant in first-order systems and is fundamental knowledge for individuals working with control systems. The other options represent different percentages that do not align with the established definition and thus do not accurately reflect the behavior of a first-order system over time.