. The Bell System technical journal . al, this method lacks 466 BELL SYSTEM TECHNICAL JOURNAL the flexibility of bridges of type 1, obtained by their unequal ratioarms. On the other hand, the use of substitution to measure theresistance or conductance component of the unknown has many ad-vantages, the principal one being that it allows the choice of a typeof bridge which will give directly the reactance component of theunknown in terms of an adjustable resistance and then by use ofthe substitution method to balance the resistance or conductanceof the unknown by means of a second adjustable res
. The Bell System technical journal . al, this method lacks 466 BELL SYSTEM TECHNICAL JOURNAL the flexibility of bridges of type 1, obtained by their unequal ratioarms. On the other hand, the use of substitution to measure theresistance or conductance component of the unknown has many ad-vantages, the principal one being that it allows the choice of a typeof bridge which will give directly the reactance component of theunknown in terms of an adjustable resistance and then by use ofthe substitution method to balance the resistance or conductanceof the unknown by means of a second adjustable resistance, thusobtaining the ideal method of balance, using two adjustable re-sistances. For the purpose of illustration, the case of the measurement of aninductive impedance may be taken. In general, the most desirablemethod would be to balance the reactance by means of series can be done by means of the bridges of Figs. 2e or 2g. ChoosingFig. 2e as the preferred form, the bridge would normally take theform of Fig. Fig. i—{a) Bridge of type 2 for measuring self-inductance, {b) The same bridgemodified by the use of partial substitution. For normal operation, Cad and Rad would be the adjustablestandards. The series inductance of the unknown would be givendirectly as KRad, while the series resistance would be given as K/Cad-This measurement of the series resistance requires an adjustablecapacitance and a computation due to the reciprocal relation. Nowsuppose a fixed value for Cad were used and an adjustable resistancestandard Rs placed in series with Zx, giving the form of Fig. 3b, inwhich Rad and Rs are the adjustable standards. If terminals Zx areshort circuited, the conditions for balance are Rs = K/Cad and BRIDGE METHODS OF MEASURING IMPEDANCES 467 Rad = 0. Then the unknown Zx is inserted and the bridge re-balanced. The inductance of the unknown is given, as for Fig. Za,as KRad, but since Cad is unchanged the total resistance in CD isunchanged. Therefore,
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