Electrophysiology is the study of electric phenomena in biological systems, dead or alive. The connection between 'electricity' and 'life' was made in the 18th century by Senor Volta who played with frog's legs and batteries and saw leg movement caused by electricity. (Frankenstein is another example).
Movement of ions across biological membranes (e.g. the uptake of K+ ions from the soil in a plant root or the entry of Na+ ions during a nerve action potential) constitutes an electrical current which we can measure by using electrophysiological techniques such as patch clamp. This allows us to study transport proteins in the membrane that are responsible for these currentts.
During patch clamping the electrode is sealed to the membrane. In this way, a small patch of membrane is electrically isolated and currents through it can be determined. The main advantages of patch clamping are the high resolution in time and current. This means that currents through one ion channel can be recorded and thus the characteristics of one protein molecule determined.
Below is an example of an actual recording of a potassium channel in the root plasma membrane of Arabidopsis thaliana. The traces depict how the current fluctuates in time when a channel opens and closes. As you can see, the channel only stays in the open (o) or closed (c) configuration for a few ms at a time. During the open state a current of approx 1 pA (10-12 A!) goes through the channel when measured at 120 mV. At 40 mV the current is roughly a third of this or 300 fA (10-15 A).