The transient current through an array of as many as 1000 quantum dots is simulated with two newly developed quantum mechanical methods. To our surprise, upon switching on the bias voltage, the current increases linearly with time before reaching its steady state value. And the time required for the current to reach its steady state value is proportional to the length of the array, and more interestingly, is exactly the time for a conducting electron to travel through the array at the Fermi velocity. These quantum phenomena can be understood by a simple analysis on the energetics of an equivalent classical circuit. An experimental design is proposed to confirm the numerical findings.