time constant

In physics and engineering, the time constant usually denoted by the Greek letter , (tau), characterizes the frequency response of a first-order,  linear time-invariant (LTI) system. Examples include electrical RC circuits and RL circuits. It is also used to characterize the frequency response of various signal processing systems –  magnetic tapes, radio transmitters and receivers, record cutting and replay equipment, and digital filters – which can be modelled or approximated by first-order LTI systems.
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Noun
1. (electronics) the time required for the current or voltage in a circuit to rise or fall exponentially through approximately 63 per cent of its amplitude
(hypernym) time interval, interval
(hyponym) relaxation time
(classification) electronics
2. the ratio of the inductance of a circuit in henries to its resistance in ohms
(hypernym) ratio

The interval required for a system or circuit to change a specified fraction from one state or condition to another. Note 1: The time constant is used in the expression where A (t ) is the value of the state at time t , A (0) is the value of the state at time t = 0, a is the time constant, and t is the time that has elapsed from the start of the exponential decay. Note 2: When t = a , A (t )/A (0) = 1/e, or approximately 0.37, and the system has changed about 63% toward its new value in one time constant. A system is considered to have changed its state after the elapse of three time constants, which corresponds to a 95% change in state. For example, if an electrical capacitor, having a capacitance of C farads, is discharged through a resistor, having a resistance of R ohms, the capacitor will be approximately 95% discharged after the elapse of 3RC seconds. Note 3: Time constants are expressed in seconds, such as 3.5 × 10-6 seconds, i.e., 3.5 s. [From Weik '89]