> 
Alternating Currents in Wheatstone’s Bridge. 
BYs Ms ES RICE: 
For the solution of problems involving continuous currents in a 
net work of conductors, two general laws suffice, viz. Kirchhoff’s 
Laws which are, (1) In any net work of conductors the algebraic 
sum of all the currents flowing to or from a junction is zero. (2) 
The sum of all the E. M. F.’s in aclosed circuit equals zero if the E. 
M. F. consumed by resistance, IR, is also considered as a counter 
E. M. F., and all the E. M. F.’sare taken in their proper direction. 
But when the corresponding problem involving alternating cur- 
rents is met with, these laws do not apply except to the instantane- 
ous values. Hence, in general, the solution of such problems re- 
quires the solving of several differential equations more or less 
involved; these equations often being too complicated for solution 
except in special cases. 
This lack of generality in the application of Kirchhoff’s laws has 
been overcome by Mr. C. P. Steinmetz who has shown *that if the 
algebra of the plane instead of that of the straight line be em- 
ployed, the laws are entirely general. 
In this method, electromotive forces, currents, and impedances, 
(corresponding to resistances for continuous currents), are all ex- 
pressed as complex quantities, e. g.; a+jb, where j=1 —r. Thus 
the absolute value of the quantity, its modulus, is } a?-+-b? and its 
: 5 b 
phase angle, its amplitude, is tan !_. 
a 
Kirchhoff’s laws may accordingly be written: 
(1) Ata junction point SI—o. 
(2) Ina closed. circuit SIZ—E, 
Saal 193 
~ 
where E=e-+ je’, |E|=Ve 
I=i+ ji, [IJ=vV i2+i 
zhi aps) || Allen a oe 
*See Proceedings of the International Electrical Congress at Chicago, 1893, pp 33-75; 
also “Alternating Current Phenomena,” Steinmetz, issued in 187. 
(31) KAN. UNIV. QUR., VOL. VII. NO. 1, JAN. 1898, SERIES A. 
