RESISTANCE AND CAPACITANCE IN SERIES 



of constant current i ^ I cos ojt (Figure 3.12) we have v^b = Vr + Vq. 

 Now Vji = IR cos ojt and we have seen that Vq = (IlcoC) . sin cot. 

 The question is how to add these to find v^^- We could do it by plotting 



is 1 cos cut 



B 



Figure 3.12 



out Vji and Vq, and adding the ordinates for a number of values of cot {Figure 

 3.13). We should then find y ^^ to be another wave of sinusoidal form and 



-*^-^ 



(^fl^^c) 



Figure 3.13 



of phase intermediate between Vj^ and Vq. If it is found to lag by an angle 

 (f) behind the curves for / and Vj^, then it may be expressed as 



UB 



= A cos (cot + ^) 



cf) is called the phase angle for the network and is the angle between the waves 

 of terminal voltage and current; it lies between and 90 degrees. A is called 

 the modulus of f ^^. The modulus of a wave refers to its amplitude, and says 

 nothing about its phase; it may be written [vj^b^ which is read as 'mod v .^b- 

 There is another, more sophisticated, approach which gets the answer a 

 good deal quicker. The quantities sin cot and cos cot may be regarded as 

 being generated by the projections of a unit vector, rotating in the plane of 



cos ujt 



Figure 3.14 



the paper at oo radians per second, on to vertical and horizontal axes (Figure 

 3.14). Then cos ojt and sin cot may themselves be regarded as vectors, 

 associated with perpendicular directions. Thus when cos cot is multipHed 



31 



