608 Appendix C 



charged, positive charges flow to one conductor and away from the 

 other. In an alternating current, the capacitors are continually 

 charged, discharged, and then charged in the reverse direction, thereby 

 effectively transmitting an alternating current. Because the charge on 

 the capacitor is proportional to the voltage across the capacitor, the 

 current through the capacitor must precede the voltage changes across 

 it. In an alternating circuit, the current through a capacitor leads the 

 voltage across it by 90°. 



An element in which the current lags the voltage by 90° is called an 

 inductance L. If a coil is formed, it is found that an emf E is induced 

 in it, as the current changes. This emf is so directed that it opposes 

 the current change. The self-inductance L is defined by 



dt 



An inductance does not alter a steady direct current but hinders the 

 flow of an alternating current. 



Many of the interesting bioelectric phenomena involve currents and 

 potentials which change in time. As was mentioned in Chapter 1, any 

 complicated function of time can be represented as a sum of terms at 

 single frequencies, or at worst, an integral of a frequency distribution 

 function. Thus, if one can describe the behavior of any circuit element 

 as a function of frequency, one can compute its response to a transient. 

 Accordingly, it is useful to be familiar with the terminology applied to 

 sinusoidal alternating currents. 



Such an alternating current, just as an alternating acoustic pressure, 

 may be described by an expression such as 



/ = A cos (cot + <p) (1) 



where A and 99 are constants and to is 2-rr times the frequency. It is 

 often more convenient to treat the measured current as the real part of 

 the complex current 2 



/ = v wt 



where the complex current amplitude is related to Equation 1 by 



/o = Ae>« (V) 



Using a similar complex notation for the potential V, one may form 

 the complex ratio 



V V„ 

 Z = j = T ( 2 ) 



2 It is important not to confuse the electronic charge e with the base of the 

 natural logarithm e = 2.7182818 .... The latter occurs in Equation 1'. 



