I am still very much a beginner in the field of electrochemistry, however, I believe that what you have created is an electrolytic cell. This is due to the application of an external current which is driving the redox reaction to work in a non-spontaneous manner. The process which is occurring is known as electrolysis, and essentially the copper strip is acting as the anode in this system, and the zinc strip (the article being electroplated) acts as the cathode per say.
Faraday wrote a physical law which describes this process: Q = It = zFn, where Q is the charge, I is the current, t is the time, z is the change in oxidation state (2), F is Faraday's constant, and n is the amount of substance oxidised or reduced.
KungKemi