aikavakio

Aikavakio, or time constant, is a measure of how quickly a dynamic system responds toward its steady state after a change in input. It characterizes the speed of the response in first-order systems and is widely used in electronics, control theory, and thermal processes to describe how fast a system reacts.

In electronics, the term is common for RC circuits. For a resistor R in series with a capacitor C charged by a step input, the time constant is tau = RC. The capacitor voltage follows Vc(t) = Vin(1 − e^(−t/RC)), and the current decays as I(t) = Vin/R · e^(−t/RC). After a time equal to tau, the capacitor reaches about 63% of its final value; after 3 tau it reaches about 95%, and after 5 tau it is over 99%.

For general first-order linear systems, the time constant sets the exponential rate at which the state variable approaches its steady state. In higher-order systems, time constants are associated with the poles of the system; the dominant pole often governs the effective time constant and the initial speed of response.

Applications span RC filters (low-pass and high-pass), charging and discharging processes, and many control and thermal systems. A common practical rule is to estimate response speed using multiples of the time constant; however, the concept has limitations for non-monotonic or multi-pole responses where several time constants interact.

Examples include an RC network with R = 1 kΩ and C = 1 μF, yielding tau = 1 ms, and a thermal system where tau equals the product of thermal resistance and thermal capacity.