EFFECT OF CAPACITY. 101 



and may be obtained by a similar construction to that given 

 on page 13 for finding the " rate of change " of a current. 

 Since in this case the rate of change is measured per radian, 

 instead of per cycle, the maximum height of the curve 

 obtained is equal to the maximum height of the curve of 

 voltage. The maximum rate of change of volts per cycle 

 would be 2 TT times as great. Curve III. is the charging 

 current plotted to a scale of amperes, each value being 

 obtained from curve II. by multiplying by the factor -125, 

 which is equal to the product of the capacity of the con- 

 denser ( = 200 microfarads) and 2 if n the number of radians 

 per second at a frequency of 100. The maximum current 

 is thus found to be 3-14 amperes. 



If E = maximum value of voltage 

 then instantaneous value of voltage = E sin 6 

 and instantaneous value of rate of change of voltage 



= E sin (0 + 90) = E cos 6. 

 Hence value of current at any instant = K E cos 6. 



It will be seen, both from the figure and from the 

 expressions just given, that the variation of the charging 

 current will be similar to those of the voltage in character, 

 but will always occur one-quarter period earlier in phase. 

 Hence the charging current will be similar to the idle current 

 discussed on page 74, except that its phase is period before 

 that of the voltage of the circuit instead of being period 

 later. By the same reasoning as that given previously it is 

 evident that the charging current is a wattless or idle current. 



In a circuit possessing both capacity and resistance there 

 will be a resultant current and voltage differing in phase. 



In a circuit possessing both capacity and resistance two 

 currents will arise when an electromotive force acts on the 

 circuit, viz., (1) the energy current in phase with the voltage, 

 (2) a charging current leading the voltage in phase by 

 period. The total current flowing at any instant will be 

 the algebraic sum of the instantaneous values of these two. 

 The resultant current may therefore be represented by a 

 rotating line obtained in magnitude and relative phase as the 

 diagonal of a rectangle having the maximum value of the 

 two component currents as the length of its sides. The 

 reason in this case follows exactly as in the case of the 

 resultant of two electromotive forces given on page 32. 



