AC Bridges

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A.C. Bridges are essential circuits used for the precision measurement of AC resistance, capacitance, and inductance, employing alternating current in their operation. Unlike direct-current circuits, where balance requires equality in resistance, these circuits incorporate both magnitude and phase balance in their measurements due to the reactive components introduced by capacitance and inductance.

Figures (16)

Inductances and capacitances can also be measured by a similar four-arm bridge, as shown in Fig. 16.1 (b); instead of using a source of direct current, alternating current is employed and galvanometer is replaced by a vibration galvanometer (for commercial frequencies or by telephone detector if frequencies are higher (500 to 2000 Hz)). The condition for balance is the same as before but instead of resistances, impedances are ed i.e.

that for balance relations, the phase balance depends on the remaining two arms. If a coil of an unknown impedance Z, is placed in one arm, then its positive phase angle @, can be compensated for in either of the following two ways:

It is a very important and useful modification of the Maxwell-Wien bridge described in Art. 16.3. In this method, the unknown inductance is measured in terms of a known capacitance and resistance, as shown in Fig. 16.7. The balance conditions for this bridge may be easily obtained by converting the mesh of impedances C, R, and R, to an equivalent star with star point O by A/y transformation. As seen from Fig. 16.7 (b). 16.4. Anderson Bridge

Example 16.2. The arms of an a.c. Maxwell bridge are arranged as follows: AB is a non- inductive resistance of 1,000 Q in parallel with a capacitor of capacitance 0.5 uF, BC isa non-inductive resistance of 600 Q CD is an inductive impedance (unknown) and DA is a non- inductive resistance of 400 Q. If balance is obtained under these conditions, find the value of the resistance and the inductance of the branch CD.

Solution. The circuit diagram and voltage vector diagram are shown in Fig. 16.8. As seen, I, s vector sum of I, and I,. Voltage V, =1, R, =1, X,. Also, vector sum of V, and V, is V as well is that of V, and V,. I, is at right angles to V.,.

This method is capable of precise measurements of inductances over a wide range of values from a few micro-henrys to several henrys and is one of the commonest and the best bridge methods.

It 1s also a modification of the Maxwell-Wien bridge and 1s particularly useful 1f the phase tan '( L/R) is large. The network is shown in Fig. 16.10. It is seen that, in this case, a comparatively smaller series resistance R, is used instead of a parallel resistance (which has to be of a very large value). angle of the inductive impedance _,, The symmetry of expressions should help the readers to remember the results even when branch elements are exchanged, as in Ex. 16.5.

It is also a modification of the Maxwell-Wien bridge and is particularly useful if the phase

The arrangement of this bridge is shown in Fig. 16.12. In this method, also, the inductance is determined in terms of resistance and capacitance. This method has, however, the advantage of being useful over a very wide range of inductances with capacitors of reasonable dimensions. Dolanna panditinn ic FJ -7F 7

It is one of the very important and useful methods of measuring the capacitance and dielectric loss of a capacitor. In fact, it is a device for comparing an imperfect capacitor C, in terms of a loss- free standard capacitor C , [Fig. 16.16 (a)]. The imperfect capacitor is represented by its equivalent loss-free capacitor C, in series with a resistance r [Fig. 16.16 (b)]. For high voltage applications, the voltage is applied at the junctions shown in the figure. Th junction between arms 3 and 4 is earthed. Since capacitor impedances at lower frequencies ar much higher than resistances, most of the voltage will appear across capacitors. Grounding of th junction affords safety to the operator form the high-voltage hazards while making balancin: adjustment in arms 3 and 4.

16.10. Schering Bridge

The balance conditions may be obtained in the usual way. For balance