Construction of Hay Bridge
The figure below is showing the general structure of a Hay Bridge. Here, across the arm AB there is a capacitor of capacitance C1 along with a very small resistance R1 in series with it. Now we connect the coil of unknown impedance in the opposite arm, that is arm CD. Besides that, we keep the remaining two arms BC and DA, entirely resistive with two known resistances R2 and R4.
We told earlier in this article that this bridge is a variation of Maxwell Wien Bridge. So, it is necessarily an AC Bridge. Hence, the balanced condition of a Hay bridge is the same as that of a general AC Bridge.
The bridge circuit is a general AC bridge shown just above. Let us write down the general balanced conditions of the AC Bridge.
Comparing with the general circuit of an AC Bridge we can write down the impedance of each arm of the above shown Hay Bridge as.
Hence, at the balanced condition,
Now, by equating the real and imaginary parts of the equation with zero we get,
From here we get,
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