1418 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1953 

 MEASUREMENT OF CURRENT 



The instantaneous value of current in a circuit being cycled by the 

 A contact is measured by inserting the primary of a toroidal air core 

 transformer in series with the circuit as shown in Fig. 2. The secondary 

 is connected to the meter through the B contact. The best design consists 

 of a secondary occupying half the winding volume and wound to the 

 same resistance as the meter. The primary can be wound in two sections 

 half inside and half outside of the secondary to provide maximum mutua 

 inductance, of a wire coarse enough to provide the number of turns for i 

 convenient meter deflection. In an air core transformer, the magnetic 

 circuit is Hnear and the flux exactly proportional to the current, a situa 

 tion that does not exist when magnetic materials are present. Because 

 of this linearity, the analysis can be made in terms of inductances anc 

 currents rather than flux linkages and currents. 



By definition, the voltage induced in the secondary of a linear trans 

 former is related to the primary current, through the mutual inductance 

 M by the relation: 



which corresponds exactly to (1) with M substituted for N, and i for (p 

 Hence, the instantaneous current at time ti is given by the relation 



where the other symbols have the same significance as before. This rela 

 tionship makes the calibration of the mutual inductance easy by setting 

 up a battery and resistor for the primary circuit and measuring the 

 steady state current with an ammeter. Then when the A contact i; 

 being switched and the instrument current /o is read, corresponding te 

 the known final primary current i, relation (8) can be solved for M. 



MEASUREMENT OF FLUX USING A BRIDGE CIRCUIT 



The search coU method of measurement just described is preferrec 

 because of the absence of any dc voltage in the meter circuit. However 



AIR-CORE 

 TRANSFORMER 



^TEST B C 



WINDING L J 



M 



Fig. 2 — Circuit for the measurement of current. 



