The time constant (T) of a circuit is the time it takes that circuit to reach 1 -1/e (about 0.632) of its final value of current or voltage if increasing. (Or, if decreasing, 1/e, about 0.368)
T is given by capacitance in farads x resistance in ohms.
In your case 4.7/1000000 x 8200 = 38.54 milliseconds