45. With the multiplier initially set for the appropriate range, a bridge balance is easily attained by a joint manipulation of the henrys and Q dials.
A balance of this Maxwell bridge is indicated by the two simultaneous equations :
wherein Ci is the standard capacitor, Ri the resistance (small rheostat) in parallel with Ci, R2 is the large rheostat and R3 is the multiplier value used. Starting with a fixed Cj value, since R2 is uniquely in Equation (3) the large dial can be calibrated in terms of Lx for a specific R3C1 product, while changing the multiplier jR 3 by a double decade step modifies one hundredfold the magnitude of Cx for any specific R •> value. Likewise, the existence of R\, in Equation (4) only, permits the small dial to be calibrated in terms of Qx for a specific value of frequency f, — in this case one kilocycle.
Parenthetically, Equation (4) sets a maximum limit to the Qx value attainable, with a specific fC product, as determined by the maximum resistance R\ for which it is practical to wind a calibrated rheostat. Higher values of Qx may be measured by the Hay bridge in which the standard capacitor and the small-valued Q rheostat are in series. The Hay bridge, however, requires a troublesome correction factor to be applied to the inductance scale values of low Q inductors. Hence the Maxwell bridge was chosen for this purpose, on the assumption that rarely do the 1-kc Q values of inductors exceed 45.
It should be noted that when iron-cored inductors are measured on such a bridge as this, having no control over the applied generator voltage, the L and Q values obtained are the 1 kc values corresponding to an arbitrary degree of magnetization in the core which is indeterminate unless a vacuum-tube voltmeter is applied across the terminals of the inductor in the balanced bridge. If the ferromagnetic core does not contain an appreciable air gap, this indeterminate magnetization will, in general, considerably exceed that corresponding to initial permeability.
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