190 
IOWA ACADEMY OF SCIENCE Vol. XXIV, 1917 
These facts are clearly brought out in figure 23 (c) in which 
is plotted the curve representing the variation with change of 
frequency of the admittance 1 of the series portion of the cir- 
cuit represented diagrammatically in the figure. Figure 23 (b), 
which is a polar diagram, shows the admittance plotted vectori- 
ally. It shows that at a frequency of thirty cycles the current 
leads the applied voltage by nearly ninety degrees. As the 
frequency is increased the phase angle becomes less and the cur- 
rent greater, the change in both being very pronounced in the 
neighborhood of the resonance frequency, which is a trifle less 
than sixty cycles. 
Just the opposite occurs in a circuit in which the inductance 
and capacitance are in parallel. The current becomes a mini- 
mum at resonance, lags for low frequencies and leads for high 
frequencies. This is brought out in figure 23 (c), and in the 
polar diagram, figure 23 (a). As it is not practicable to draw 
a large number of vectors in this and other figures only a few 
are shown. The end points of a few more are indicated by 
large dots marked with the corresponding frequency. These 
are sufficient in number not only to determine the hodograph 
which is shown as a heavy continuous line but also to enable 
one to estimate the vector corresponding to any frequency. 
lr The admittance of an alternating current circuit is that factor which 
multiplied hy the applied voltage gives the current. It is therefore pro- 
portional to the current and equal to the current flowing with unit voltage 
impressed on the circuit. 
