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IOWA ACADEMY OF SCIENCE Vol. XXIV, 1917 
of current may be controlled by a variation in the reactances 
of the series circuit. 
It is quite difficult to see the effect of a change in the con- 
stants of the parallel circuit. In general we may say that with 
increase of resistance in the branches the end points of the 
impedance vectors are crowded around on the hodograph to- 
ward the axis, so that the circuit becomes less sensitive to 
changes in frequency. If, however, the resistance is small the 
crowding is at the ends and the impedance sweeps around 
through a large angle with a very slight change of frequency 
in the neighborhood of resonance and the change for extreme 
frequencies is correspondingly smaller. A change in the re- 
actance tends to make the whole figure smaller or larger, but 
unless the resistance is changed in the same proportion the 
character of the figure will be altered as already explained. 
The control of the power-factor is of course dependent upon 
the same factors as the control of the current. If the power- 
factor is to be made to remain at values close to unity over a 
wide range of frequency it is necessary that the “wound up” 
portion of the impedance hodograph represent a large part of 
the total frequency variation. This may be done by decreasing 
the reactances of the series branch. If, on the contrary, the 
series reactances are made greater the range over which the 
power-factor is practically unity is made smaller but over this 
range the power-factor remains very much closer to unity. 
Thus far we have interpreted the circuit from the standpoint 
of impedances. It is very helpful to study the relations of the 
current to the voltages over the two portions of the circuit and 
to see how the current divides in the parallel circuit. Plate 
X, (g) shows how the branch currents vary with frequency, and 
they, together with the total current, are plotted vectorially with 
the voltage over the parallel circuit as the axis of reference. 
One notices that the current in the condenser branch always 
leads by a large angle and that the current in the coil branch 
lags by a large angle. It is evident that the changes in phase 
and magnitude of the two currents, as the frequency changes, 
are just opposite. When the branch currents are added vec- 
torially, frequency by frequency, the total current hodograph 
is obtained. The lengths of these total current vectors are equal, 
at each frequency, to those of diagram (f). The difference in 
