DIELECTRIC PROPERTIES OF INSULATING MATERIALS 509 



In equations (11) to (13a) e', e" and 7' are expressed in e.s.u., while 

 Cp and Co are expressed in farads and Gp in mhos. The substitution 

 of the frequency, /, for oj in (13a) depends upon the fact that/ = 27rw. 

 While it is usual to express e' and e" in e.s.u., it is more convenient 

 for most purposes to have 7' in the units ordinarily used for specific 

 conductance: thus when expressed in ohm"^-cm~^ 



7-. '^ = ''f , (14) 



^ 47r X 0.9 X 1012 1.8 X 10^2 ^^^; 



8.85 X 10-2 ^ 



= — r ^p = -J ^P' (14^) 



v-o mmf -^ 



where Co mmf is the capacitance in micromicrofarads. 



By expressing equation (8) in the equivalent polar form certain 

 quantities appear which are closely related to 7', e' and e" and which 

 are commonly used in describing the characteristics of dielectrics. 

 The polar form is 



7 = 7oe'^ 



where 70 = (7' + y"^y'^, a quantity which is a measure of the 

 amplitude of the complex current in the dielectric for unit voltage 

 gradient, while 6 — tan^^ t'Vt' is its phase angle. It is customary 



to use the loss angle which is defined as I — — ^ J =8, rather than the 



phase angle in the description of dielectric properties. It is evident 

 that 8 = tan -^ 777" = tan-^ e'Ve' and that 



tan 8 = Gp/Cpoo. (15) 



Similarly, the power factor is given by 



cos e = 77(7" + 7"')i/2 



= e"l{e" + e"'y'' = Gp/{Gp' + CpWy^. (16) 



When the current given by (8) is multiplied by the voltage, Eq cos oot, 

 we obtain the instantaneous power, and from this the mean power W 

 can be obtained by integration over a whole number of half periods. 

 We then obtain 



trperseco„d = y (1)^ = ^(1)' (16«) 



and 



F per cycle = '-^ (^J . (166) 



