Time constant ( $e^{- t / τ}$ )

The time constant

τ > 0

in exponential decay is the time over which the decaying quantity is multiplied by

e^{- 1}

. A response approaching equilibrium as

q (t) = q_{\infty} + (q (0) - q_{\infty}) e^{- t / τ}

has the same time constant. For a resistor-inductor circuit it is

L / R

.

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The time constant is a measure that characterizes the time response of a system, typically in the context of first-order linear systems, such as electrical circuits (like RC circuits) and mechanical systems (like damped harmonic oscillators). It provides a way to quantify how quickly a system responds to changes in input.

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