## Hay’s Bridge

It is also a modification of the Maxwell-Wien Bridge and is particularly useful if the phase angle of the inductive impedance **ɸ _{m} = tan^{-1}(ωL/R)** is large. The network is shown in figure 1. It is seen that, in the case, a comparatively smaller series resistance R

_{1}is used instead of a parallel resistance (which has to be of a very large value).

Here

**Z _{2} = R_{2}**

**Z _{3} = R_{3} + jωL_{3}; Z_{4 }= R_{4}**

Balance condition is **Z _{1}Z_{3} = Z_{2}Z_{4}**

Separating the reals and the imaginaries, we obtain

Solving these simultaneous equations, we get

The symmetry of expression should help the readers to remember the result even when branch elements are exchanged.

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sometimes in Hay’s bridge inductor used in parallel with resistance. why?