222 SPEEDS OF SOME PROCESSES IN BIOLOGICAL SYSTEMS 



The conductivity of a solution increases with increasing area and decreas- 

 ing length of path. That is, it is given by 



A 



K — 



L 



This, of course, is the inverse of resistance, which equals 



(\/k)(L/A) =(R(L/A) 



where (R is the specific resistance, or the resistivity. 



Example: Calculate the electrical conductivity of a finger. A typical body 



solution contains about 100 meq of KC1 per liter. The finger is about 10 cm 



long and 4 cm 2 in cross-sectional area. 



A 4 



Conductance = k — = 129 x 0.1 x — = 5.2 ohms ' 



L 10 



Resistance (= 1 /conductance) = 1/5.2 = 0.2 ohms 



Current driven through this column of solution by 1 10 v applied across the 

 ends would be: 



i = 110/0.2 = 550 amp 



Hence body fluids are relatively good electrical conductors. By contrast, 

 skin is relatively a very good insulating material, and provides a measure of 

 protection against electrical shocks. It is estimated that 1 ma of total body 

 current does irreparable internal damage. However, the calloused fingers of 

 some electricians are legendary in this respect: some will span the contacts 

 of a 1 10 v circuit with two fingers and allow the ''tickle" to tell them whether 

 or not the circuit is complete! 



Difference in electrical mobility is the basis of electrophoretic separation 

 of macromolecules, such as the globulins in solution. In Table 8-9 are some 

 values which illustrate this. Characterization of the hemoglobins by this 

 property was illustrated in Table 6-5. There it was called "/." Both / and \i 

 are commonly used symbols for mobility. 



The "Volume Conductor" 



In a volume of electrolyte, the paths taken by the current depend upon the 

 geometry (see Figure 8-15). Consider the two cases illustrated: (1) in a 

 cylinder full of electrolyte, with glass walls and metal ends, the paths will 

 be parallel; but (2) if the potential source is small relative to the electrolyte 

 volume, the current paths diverge from the positive and converge back to the 

 negative. Only two dimensions are represented in the figure, but the argu- 

 ment would be the same for three. 



Analogy with metal electrical circuits is usefully drawn, for in metals the 

 carrier is the electron cloud. Ohm's law is obeyed by electrolytic conductors 



