The alternating current bridges are mainly designed to measure the electrical quantities such as inductance and capacitance. These AC bridges are the improved versions of Whetstone Bridge. These bridges in their basic form consist of normally four arms, an AC power source and a detector. The Maxwell’s Inductance Bridge is one such type of bridge normally used for measurement of inductance whose ‘Q’ values lies below ’10’.
The Maxwell’s Inductance Bridge is most commonly used bridge for measurement of inductance so f Q value below 10. A typical Maxwell’s bridge consists of an inductance measured in comparison with a capacitance in laboratory operations. The input for the bridge is given through a standard 1 KHz oscillator circuit which produces a 1 KHz sine wave at constant amplitude. The basic circuit diagram is as shown below.
Now let us see the derivation for calculating the unknown value
Let L4 = Unknown inductance
R4 = Effective resistance of inductor L1.
R2, R3,R4 = Known non – inductive resistances
C2 = Variable standard capacitor.
At balanced condition,
→R4R2 + jω L4R2 = R1R3 + jωR1R2R3C2
Now separating real and imaginary terms, we have
The expression for Q factor is given by
The Maxwell’s bridge is limited to the measurement of medium Q coils (1<Q<10). This can be shown by considering the second balance condition which states that the sum of the phase angles of one pair of opposite arms must be equal to the sum of the phase angles of the other pair. Since the phase angle of the resistive elements in arm 2 and arm 3 add up to 0, the phase angle of high Q coil will be very nearly positive which requires that the phase angle of the capacitive arm must also be very large indeed which can be very impractical. High Q coil are therefore generally measured on Hay’s bridge.
The main advantage of the bridge is that the two balance equations are independent if we choose R2 and C2 as variable elements and also the frequency does not appear in any of the equations.
The main disadvantages of the bridge are that it requires a variable standard capacitor which is very expensive so fixed standard capacitors are used normally. To compensate this, balance adjustments are done by both varying R1 and R2 or by putting an additional resistance in series with the inductance under measurement and then varying this resistance and R2. The bridge also has a disadvantage of limited measurement of low or coil (1<Q<10) and is also unsuited for measurement of low ‘Q’ coils i.e., below 1. Hence the Maxwell’s bridge is used only for the measurement of medium ‘Q’ coils.
The unit has an inbuilt 1 KHz oscillator circuit for giving input to the bridge and an output is find the CRO in the balance condition output is zero.