These values are derived from the mathematical constant e, specifically 1 − e − 1 and e − 1 respectively.
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A resistor by itself has no time constant. For a circuit to have a time constant it must contain either capacitors or inductors.
In theory ... on paper where you have ideal components ... a capacitor all by itself doesn't have a time constant. It charges instantly. It only charges exponentially according to a time constant when it's in series with a resistor, and the time constant is (RC). Keeping the same capacitor, you change the time constant by changing the value of the resistor.
The heating time constant is the time that an induction motor takes to reach it's operational temperature.
Time constant in an RC filter is resistance times capacitance. With ideal components, if the resistance is zero, then the time constant is zero, not mattter what the capacitance is. In a practical circuit, there is always some resistance in the conductors and in the capacitor so, if the resistance is (close to) zero, the time constant will be (close to) zero.
The algorithm will have both a constant time complexity and a constant space complexity: O(1)