ajjTbrnatb current generator. 



75 



armature circuit, we find from the first expression tor E, section 10, 

 that — 



Ei = — ^- 2 2 V" (a,;-i + a^+i ) a^, ; or 

 4 



-gr-_ _ w»» C Va,a, — Va,a, + 3 Va^a, —3 V3iMi+ 5 Va^a^— 5 Vajag ") 



^'^~ "4"! +&C. ' )• 



And from the second expression for E that — 



E^ = '^i" 5 q. V (f, a,. a„ ) = ^' 5 ^ D. Vt ■^" a,.a,, 



= — 2 a,/ (7 D,, smffj = -r '^ k^ 



2r 



as D,, sin/^ = — . {See section 5). 

 qino} 



= the heat developed in the armature cii'cuit. 



Similarly the total electrical power (H + t]) $ developed in the 

 field circuit is given by — 



rja^ (am 



(H -\-ri) i = ; - -- 2p V (a„_i + ap+i) a^ 

 2 4 



j 2 V a, a,- 2 V a, a, + 4 V a, a, -4 V a^ a. + &c. > 



a - (Din 



= p 



4 4 



or by — 



(H 4- rj) ^ = p'^+ l^-(d^ + a; + «: + &c. y 



= total heat developed in the field circuit and madt^ up of two parts, 



a* 



the first = p ^ due to the direct exciting current, and the second 



T 



^1 d^ + d^ + &c. j due to the induced alternating field current. 



Adding the first expressions for E.r and (H + tj) $, and cancelling 



r]$ against p'^ we find that — 

 4 



E^ + H^= - ^ i Va,a. + Va,a, + Va,a3 + Va3a^+ &c. I 

 12. The torque exerted at any instant in driving the alterna or 



IS — 



= — a: $ — - {m cos wt) = mx $ sin Mt 

 a {u)t) 



= ^ 2 a,/ X t 1 2 (ttf/-! — ug+i),,. {See section 4.) 



