POWER LOSSES IN INSULATING MATERIALS 111 



resistance assumed negligililc.) For small angles this may be written 



P = £ / ^,1 



= 2Trf E^aK ^, 



since I = 2 irf E C, f being the frequency. 



In the particular case of a condenser of two parallel plates 



A 

 a = m—r> 

 a 



where w is a constant depending on the units used, A the area of one 

 plate, and d the thickness of the dielectric. 



Hence P = 2Tr f E'' m ^ K ^. 



Eg = — • Therefore the power loss per unit volume is 



But the volume of dielectric V = A d, and the voltage gradient 

 E 

 d' 



^ = m'E,'fK-^, (1) 



where m' = 2 -k m, and m' K ^ = loss per unit volume at unit 

 frequency and potential gradiant. 



Thus it is seen that while no single factor of the expression can be 

 used to represent the losses, the product of phase difference and di- 

 electric constant ^ can be used in this way. Furthermore, for most 

 good insulators, this product remains fairly constant throughout a 

 considerable range of voltage and frequency. For example, we have 

 found that for such materials as wood, phenol fibre, and hard rubber, 

 the change of this product with frequency is of the order of 20 per cent 

 from 200,000 cycles to 1,000,000 cycles. Hence it is possible to com- 

 pare directly the losses in different materials even though the measure- 

 ments were not made at exactly the same frequency. 



If ^ is taken in degrees. Eg in volts per centimeter, and/ in cycles 

 per second, the constant w' reduces to 0.97X10."^*. Hence, for a 

 frequency of 1,000,000 cycles per second and a potential gradient of 

 10,000 volts per centimeter, the product of K and "^ (in degrees) is 

 within 3 per cent of being numerically equal to the dielectric loss in 

 watts per cubic centimeter. 



1 The substitution of the angle for its sine is correct to better than 5 per cent 

 for angles as large as 30°. 



- This relation has been brought to the attention of the Committee on Electrical 

 Insulating Materials of the American Society for Testing Materials and is included 

 in their "Tentative Method of Test for Phase Difference (Power Factor) and Di- 

 electric Constant of Molded Electrical Insulating Materials at Radio Frequencies." 



