74 Dr. McLachlan on Effective Inductance, Effective 



Now the apparent permeability of the iron varies with 

 the current flowing through the coil, and this causes a 

 variation in the effective resistance, the periodic time, and 

 also the shape o£ the voltage and current waves. It is 

 essential, therefore, that in order to* treat the subject at 

 all, some assumptions must be made with regard to the 

 above variables. The simplest method is to assume the per- 

 meability and the effective resistance to be constant, with a 

 given capacity in circuit, from which it follows that the- 

 oscillation is of the form <? _A ^sin (cot + 0). 



L e = effective inductance, assumed constant. 

 E e = effective resistance, assumed constant. 

 C = capacity of condenser. 

 \ = R e /2L e . 



r = voltage on condenser at any instant. 

 v L = ,, „ inductance „ 



v r = „ ,, resistance „ 



i = current at any instant. 

 V = maximum voltage on condenser. 



Then it can be shown in the usual manner that the 

 Instantaneous voltage on condenser, 



Bo = vi^^ 2 )V* i sin(»i + 6>) .... (13) 



Instantaneous voltage on resistance 



w r = V CU(^^J.e- w sin'(f»* + 9r) . \ (14) 



Instantaneous voltage on inductance/ 

 r L = LJdi/dt) = V CL e (^^)V w sin {cot- 6) • (15) 



where 



_JL Ik! 

 L.C 4L„ 2 * 



Now the vector sum of the e.m.f.'s round a closed circuit 

 is zero : hence we can represent the e.m.f.'s of the circuit of 

 fig. 20 at any instant as shown in fig. 21. 



