ON ELECTRICAL CONDUCTANCE; EEG AND EKG 



223 



EKG 



equipotential 

 surface 



Figure 8-15. "Volume Conductors." Top left: Metallic. Center and Bottom 

 Left: Electrolytic, with parallel (1) and diverging and converging (2) current 

 paths. (2b) shows current density and resistance per unit area along current 

 paths as a function of radial distance, x, from the straight line joining the 

 sites (A and B) of potential difference. Top right: Positions of electrodes for 

 electrocardiogram and electroencephalogram. 



(V = z7?), and the voltage drop (z'/?,) over any fraction of the resistor is pro- 

 portional to the resistance, /?,, of the fraction in question. Thus (Figure 

 8-15) the total voltage drop across the resistor is iR, but is only z7?, for the 

 fraction A-b. The same arguments are true for the electrolytic case (1) 

 above. However, if the current paths diverge (case (2)), certain paths are 

 longer than others, and the resistance, per unit area, along the path is there- 

 fore higher. For a fixed voltage at the source, higher resistance means that 

 smaller current will flow through the longer paths; in fact the current density 

 (i.e., current per unit area along a path) will be high in the center, directly 

 between the plates, lower as the radial distance, x, increases. The distribu- 

 tions of current density and of resistance, per unit area, along a path are 

 shown in Figure 8-15, (2b). In the higher resistance paths on the outside of 

 the volume conductor the total potential drop, V, between A and B has to be 

 the same as in paths directly between the electrodes. In the outside paths, 

 R is higher and the current density, i/A, is lower. Nevertheless, as in the 

 metallic case, the voltage between two points, A and b, in the outside path, 

 can be measured with a good voltmeter, and that value is numerically equal 

 to the voltage between A and b' deep within the conductor. 



