14 TREATISE ON ALTERNATING CURRENTS. 



their respective E.M.F.s of mutual induction while the currents 

 rise from o to I\ and o to /2 respectively is given by 



M- + ija^f- I dt 



= Mfd(iii 2 ) = 3//!/ 2 (G) 



This together with the work done in driving the currents against 

 their respective KM.F.s of self-induction is the total energy 

 expended in creating the magnetic field, and the total energy of 

 the magnetic field is therefore given by 



W^kLitf + WJ + MIJs . . . . (7) 



This energy is stored up in the magnetic field and is restored 

 to the circuits when the currents are stopped. 



ELECTRIC CURRENTS IN INDUCTIVE CIRCUITS. 



15. CASE I. Electric Current in a Single In- 

 ductive Circuit. Let the resistance of the complete circuit 

 be r and its coefficient of self-induction L, and let a potential 

 difference e be applied between the terminals of the circuit. 



If i is the instantaneous value of the current, the instantaneous 

 value of the E.M.F. necessary to drive it against the resistance 

 of the circuit alone is, by Ohm's law 



n 



The instantaneous E.M.E. due to self-induction, and which 

 opposes the passage of the current, is 



di 



- L ~di 



The applied potential difference has, therefore, to balance the 

 E.M.F. of self-induction by providing a component equal 



to 4- L-j-' and also to provide a component equal ri to drive the 

 dt 



current against the ohmic resistance of the circuit. 

 We thus arrive at the equation 



