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It is the time required to charge the capacitor, through the resistor, from an initial charge voltage of zero to approximately 63.2% of the value of an applied DC voltage, or to discharge the capacitor through the same resistor to approximately 36.8% of its initial charge voltage.
This means that the time constant is the time elapsed after 63% of V max has been reached Setting for t = for the fall sets V(t) equal to 0.37V max, meaning that the time constant is the time elapsed after it has fallen to 37% of V max. The larger a time constant is, the slower the rise or fall of the potential of a neuron.
The article states this as a definition of RC time constant: It is the time required to charge the capacitor, through the resistor, by ≈ 63.2 percent of the difference between the initial value and final value or discharge the capacitor to ≈36.8 percent.
That is, τ is the time it takes V L to reach V( 1 / e ) and V R to reach V(1 − 1 / e ). The rate of change is a fractional 1 − 1 / e per τ. Thus, in going from t = Nτ to t = (N + 1)τ, the voltage will have moved about 63% of the way from its level at t = Nτ toward its final value.
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
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