I would like to measure time period of very short periods of electricity flow in the range of micro seconds or even smaller;can someone tell me me a device that can help me do this?
A digital oscilloscope is a good place to start. Will you be measuring currents or voltages or both? You might even be able to use an inexpensive USB digital oscilloscope, depending on what you are trying to measure.
I'll find the old thread where we discussed inexpensive digital oscilloscope options...
EDIT / ADD -- Here are a couple of threads that may help you learn more background...