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Essentially all RC circiuts filter of time. Annother application is
setting tyhe frequency response of FM radios (filtering). In the
FM radio business one talks about a 75 micro-second filter.
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The time constant for your components is 2.2 s, a bit short for
a DVM. Try getting a 1 farad capacitor (from Digikey for less
$10) or use the largest C and R you have.
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One time constant is the time necessary to charge a cap to 63%
of its final voltage. The 10 and 90 % points you mentioned are
used for measuring rise (and fall) times. They are related to
time constant but are not the same thing.