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AC Bridges and Theory of AC Bridge

We use these bridges for measurement of inductances and capacitances in the most accurate manner. Principally, an AC Bridge is similar to the Wheatstone bridge. Like Wheatstone Bridge, it has also four arms. Instead of using pure resistances in the arms, we use impedances in the case of an AC Bridge.

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Now suppose, Z1, Z2, Z3, and Z4 are the impedances of four arms of the bridge. Instead of using a DC galvanometer in the case of Wheatstone Bridge, we use here vibration galvanometer or detector. Instead of a battery, we use here an alternating source of voltage.

Theory of AC Bridge

Before going to the actual theory of AC Bridge, let us recall the theory of Wheatstone bridge.

Wheatstone bridge
Wheatstone bridge

As shown in the figure above, at the balanced condition of the bridge,

In this bridge, we use impedances instead of resistances. The balanced condition of an AC Bridge is the same as that of the Wheatstone Bridge. That means here we will write,

The impedance has two components in its polar form. One is its magnitude and the other is its phase angle. So, we can write the expression of the impedances, as |Z1|∠φ1, |Z2|∠φ2, |Z3|∠φ3 and |Z4|∠φ4. Now, we can write the expression of the balanced condition of the bridge circuit as,

From the above expression, we can conclude that there would be two conditions, for a balanced AC bridge with four impedance arms. Obviously, the balanced bridge must satisfy these two conditions simultaneously. And these conditions are

There are many types of AC bridges. We use them for different measurements, such as

For measuring self-inductances

For measuring capacitances

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