The capacitor in an RC-circuit begins charging at t = 0. Its charge Q can be modelled as a function of time t by
Q(t) = a
where a and tc are constants with tc > 0. (We call tc the time constant.)
A) Determine the constant a if the capacitor eventually (as t → [infinity]) attains a charge of 2000 µF (microfarads).
B) If it takes 12 s to reach a 50% charge (i.e., 1000 µF), determine the time constant tc.
C) How long will it take for the capacitor to reach a 90% charge (i.e., 1800 µF)?