110 ELECTRICAL ENGINEERING 



where CR = iR is the e.m.f. consumed by the resistance of 



the circuit, 



ex = L -r is the e.m.f. consumed by the inductance of 

 the circuit, 



ex f = 7* is the e.m.f. consumed by the capacity of the 

 O 



circuit. . 



Assuming that the impressed e.m.f. leads the current by angle 

 <, its equation is 



e = Eo sin (2irft + 0), ...... (159) 



and 



Eo sin (27T/Y + 0) = Ri + L| + 



fidt 

 = Ri + L + J-_ . (160 ) 



Differentiating with respect to t, 



2TrfE cos(27rft + <l>)=Rj t + L ( jf 2 + ^, . (161) 

 but 

 i = I Q sin 2 vfl, j = 2 TT//O cos 2 T/, ~ = - (2 7r/) 2 / sin 2 ir/ 



when 



in</), - = - (2 irf) 2 I cos <{>. 



when 



Substituting these values in equation 161, when t = 0, 

 2irfE Q COS<j> = 2<jrfRI , 



and 



JJT "[} 



(162) 



when t = 



IQ COS </> ' 



90-0 



= 2 TT/K/O sin ^ - (2 7T/) 2 7 cos + cos 0, 



