79 



On the Alteenatikg Current Dynamo. By W. E. GoLDi?BOROL"(;H. 



Consider the case of a simple alternator having but one armature coil that 

 rotates in a magnetic field of uniform intensity about an axis at right angles to 

 the direction of the lines of force. If successive instants of time during one rev- 

 olution of the coil are counted from the instant that the coil j^asses a line drawn 

 ihrough its axis of rotation and perpendicular to both the axis of rotation and 

 the direction of the magnetic flux, the value of the induction piercing the coil 

 at any instant dui'ing one cycle is expressed by the equation 



N — Nmax COSWt, (1) 



in which Nmax equals that portion of the flux that passes through the coil at the 

 instant the plane of the coil is at right angles to the direction of the lines of force 

 and «■ represents its angular velocity. The instantaneous value of the E. M. F. 

 generated in the coil will be, by Faraday's law 



dN 



e = — = IV Nmax sinwt, 



dt 

 = E sinwt (2) 



since its maximum value 



E = t(;N,„ax (3) 



If the coil is closed through a circuit of resistance Kj, inductance L^ and ca- 

 pacity C'l, the resistance and inductance of the coil, itself being R and L respec- 

 tively a current i will begin to circulate and we can write the equation of E. M. 

 Fs. of the circuit in the form 



di ridt 



e = (R + Ri)i-f (L + Li)- + J — . 

 dt Ci 



From this expression we can derive the equation of the current in terms of the 



constants of the circuit and the maximum value of the E. M. F. developed in the 



coil and obtain 



E 



V 



[R + Ri]2 -f C-;^ - IL + L,)wy 



sin i w't — tan 



LCito(R+Ri) R-f Ri Jj ^ ' 



which expresses the instantaneous value of i as soon as a condition of cyclic sta- 

 bility has been attained. 



Equations (1), (2) and (4) are the general equations that cover the working 

 of alternating current dynamos; they have been subjected to graphical analysis, 



