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 3 RC seconds. Note 3: Time constants are expressed in seconds, such as 3.5 × 10 -6 seconds, i.e., 3.5 s. [ From Weik '89 ]