24 TREATISE ON ALTERNATING CURRENTS. 



CURRENT IN A CIRCUIT OF CONSTANT INDUCTANCE WITH A CON- 

 STANT POTENTIAL DIFFERENCE BETWEEN ITS TERMINALS. 



2O, Let L be the coefficient of self-inductance of the circuit, 

 r resistance of the circuit, 

 e ,, constant P.D., 

 i current at any instant, 

 t time from the instant when the current is 



made. 



The equation from which to determine the current is (see 

 15, Chap. II.)- 



The complete solution of this equation is (see Appendix) 



(6) 



where * is the base of Xaperian logarithms, and equals 27 

 approximately. 



The exponential term occurring in the solution shows that the 



current does not theoretically attain the steady value - for an 



infinite time ; it, however, practically attains this value after a 

 very short time. 



The time T taken for i to reach the value - - is given by 



- is sometimes called the Time Constant of the circuit. 



CURRENT IN A CIRCUIT OF CONSTANT INDUCTANCE WITH AN 

 ALTERNATING POTENTIAL DIFFERENCE BETWEEN ITS TERMINALS. 



21. Let L be the coefficient of self-induction of the circuit, 

 r resistance of the circuit, 

 n frequency 

 e = E sin pt be the applied P.D., 

 p = 2-n-n, 

 i be the current in the circuit at any instant. 



