ALTERNATING CURRENTS 



probable that in the practice of the future the sine wave will play 

 as prominent a part as it does in the theory of the present. 



A sine wave may be represented either analytically, by means 

 of an equation of the form 



y = Y sin pt, 



or graphically as in Fig. 2, t being plotted horizontally and y verti- 



cally. 



with 

 of as 



PIG. 2. Sine Wave. 



There is still another mode of representation, however, very 

 generally used, and known as the vector 

 or clock-face diagram method. In this, 

 we suppose a straight line of constant 

 length OP (Fig. 3) = Y to revolve with 

 constant angular velocity p (radians per 

 sec.) about one of its extremities as 

 centre. Such a rotating line of con- 

 stant length may be termed a rotating 

 vector. Suppose that at the time t = 

 the line is in the horizontal position 

 (shown dotted in Fig. 3). After t sees., 

 it will have swept out an angle pt, so 

 that its projection on the vertical will 



be OP cos ( ^ - pt} = Y sin pt = y. 



As, therefore, the line OP rotates, its 

 projection on the vertical at any instant 

 FIG. 3.- Vector, or Clock- gives us the magnitude and sign of the 

 face Diagram. alternating current at that instant. 

 The extremity of this projection moves 



a simple harmonic motion, and the projection itself is spoken 

 an alternating vector. 



