102 KENNELLY AND VELANDER— POTENTIOMETER 



therefore pursues a straight-line locus. The current in the work- 

 ing circuit will be 



/„' = 7y amperes Z (6) 



where \E-^y\ is the constant size of the induced e.m.f. in that circuit, 

 and /?° is the angle of lag of that e.m.f. behind the current in the 

 potentiometer circuit, considered as of reference phase. This cir- 

 cuit happened, in this case, to be strongly condensive, owing to the 

 adjustment of the condenser C in Fig. i. The angle of lag /? is the 

 angle DOP in Fig. 2. In equation (6) the vector impedance Z 

 appears as a reciprocal, or in the denominator. It is well known 

 that the reciprocal of any vector straight-line locus is a circular 

 locus passing through the origin. The diameter of the circle through 

 the origin is also the reciprocal of the perpendicular distance from 

 the impedance origin to the impedance locus. Consequently, in 

 Fig. 2, with \E^y\ =y.2y2) volts, the diameter OP, expressed in am- 

 peres, will be 7.273X1/3181^0.002285 ampere, or 2.285 miHi- 

 amperes, lagging ^° behind the phase of the potentiometer current 

 OR. The measured p.d. across 100 ohms in the resistance R will 

 be 0.2285 volt, also lagging ^° . 



In reducing the capacitance of C from infinity to zero, the cir- 

 cular locus of potential across pp' has nearly covered three quarters 

 of its entire circle. It is evident from a consideration of Fig. 3, that 

 if, with the condenser shorted, additional inductance could have been 

 inserted in the circuit, while retaining all other conditions constant, 

 the remainder AO of the circular locus might also have been 

 traversed. 



The use of the new potentiometer thus enables this circular 

 potential and current locus, at telephonic frequency, to be demons 

 strated observationally, instead of remaining on a purely abstract 

 mathematical basis. 



Simple RLC Circuit of Sharper Resonance. 



Another example of varying the series capacitance in a simple 

 a.-c. circuit, but at a frequency of 201O'— ', is given in Fig. 4. Here 

 almost the entire circular locus of potential and current is covered 



