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Draw and discuss Hays Bridge and its application for measurement of inductance.

Mumbai University > Electronics and Telecommunication > Sem3 > Electronic Instruments and Measurements

Marks: 10M

Year: June 15

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Before we introduce Hay's bridge, let us recall the limitations of Maxwell Bridge. Maxwell bridge is only suitable for measuring medium quality factor coils; having said that, it is not suitable for measuring high quality factor (Q > 10). In order to overcome this limitation, we need to modify Maxwell Bridge so that it will become suitable for measuring Q factor over a wide range. This modified Maxwell Bridge is known as Hay's bridge.

Hay's Bridge Theory

As said earlier that Hay's bridge is modified Maxwell Bridge, now question is the field where modification is needed. In order to understand this, let us consider the connection diagram given below:

In this bridge the electrical resistance is connected in series with the standard capacitor. Here $l_1$ is unknown inductor connected in series with resistance $r_1$. $c_4$ is standard capacitor and $r_2$$r_3 r_4 are pure electrical resistance forming other arms of the bridge. From the theory of AC Bridge, we can write at balance point, z_1.z_4=z_3.z_2 ----------------(1) Here, z_1=r_1+j.wl_1 z_2=r_2 z_3=r_3 z_4=r_4-\frac{j}{wc_4} Substituting the values of z_1 z_2 z_3,and z_4 in equation (1) we get, (r_1+jwl_1).(r4-\frac{j}{wc_4})=r_2.r_3 \frac{(r_1.r_4+l_1)}{c_4}=r_2.r_3..................................(2) and l_1=\frac{r_1}{w^2.r_4.c_4}...........................(3) on solving equation(2) and (3) we get, Now if we substitute Q >10 then 1/Q^2 = 1/100, and hence, we can neglect this value, thus neglecting 1/Q^2 we get r_2$$ r_3$ $c_4$ which is same as we have obtained in Maxwell bridge. Hence, Hay's bridge circuit is most suitable for high inductor measurement.

The bridge gives very simple expression for the calculation of unknown inductor of high value. The Hay's bridge requires low value of $r_4$ while Maxwell Bridge requires high value of $r_4$