On the Use of Mutual Inductometers
Albert Campbell · Proceedings of the Physical Society of London · 1909
In the use of mutual inductometers (or variable inductances) already described by the Author, the use of a balancing coil in one arm of the bridge causes considerable loss of sensitivity. With an equal-arm bridge this difficulty is overcome by putting the two halves of the secondary circuit in adjacent arms of the bridge. The auxiliary balancing coil is thus dispensed with and the usual formula is still applicable. The Author next discusses the measurement of effective resistance, which is in general much more troublesome than that of self-inductance. As the effective resistance determines the total power spent by a given alternating current in a conductor, it is a most important quantity in telephonic and other high-frequency work. When it is measured by an ordinary self-inductance bridge, Giebe has shown that large errors may be introduced by the small residual inductances of the ratio arms. The Author works out the analogous formulas for mutual inductance bridges, which indicate that the inductances of the ratio arms must be accurately proportional to their resistances, if errors are to be avoided. He next describes a null method in iron testing analogous to Max Wien's self-inductance method. The ring to be tested is wound with primary and secondary coils. The magnetizing current I 1 is passed through the primary coil, the primary circuit of a mutual inductometer, and a slide-wire resistance. The detecting instrument, a vibration galvanometer or a tuned telephone, is put across a circuit consisting of the secondaries of the ring and the inductometer in opposition and a part Q of the slide-wire resistance. By adjusting Q and the reading M of the inductometer a balance is obtained, in which case the power lost in the ring (due to hysteresis and eddy currents) is equal to QI 1 2 ×N 1 /N 2 , where N 1 and N 2 are the numbers of turns in the windings of the ring. In certain cases the permeability can also be directly found. The method is immediately applicable to the testing of current transformers. If the instrument usually in the secondary circuit of the transformer be replaced by a suitable low resistance S, then when a balance is obtained tan Φ=2π n M/Q and I 1 /I 2 eq, falling dots S/Q, where Φ is the angle of lag between the primary and the reversed secondary current, and n is the frequency. The primary current should have a sine wave form. The method gives directly the two quantities wanted in practice, but, owing to considerations of wave form, the results must be interpreted with caution.