We normally use a Maxwell bridge to measure medium inductances. We can also arrange this bridge to yield the result of the measurement to a considerable precision. There are two inductive arms and two purely resistive arms in a Maxwell Bridge. This arrangement makes the bridge much simpler for operation. Because we can do the phase angle balancing only by the inductive arms.

This is essentially an AC Bridge. So, the bridge requires both the magnitude balancing as well as phase angle balancing.

In a Maxwell Bridge, we usually measure the inductance of a coil. We have to connect this coil across one of the bridge. A standard coil must have inductive as well as resistive property. Now we have to connect a variable inductance across any of the adjacent arms of the measuring coil. Then we can adjust the phase angle of variable inductance by adjusting itself only. Since the other two arms of the bridge are purely resistive, so they do not have any phase angle.

## Theory of Maxwell Bridge

At balanced condition, the phase angle of the measuring coil and the adjusted phase angle of variable inductor must be the same. The balanced condition means the potential of both ends of the detector device is the same.

We know that at the balanced condition of an AC Bridge,

Here, Z_{1}, Z_{2}, Z_{3}, and Z_{4}, are the impedance of four branches of the ac bridge respectively.

Let us consider the expression of the unknown impedance of the measuring coil is

And the expression of the impedance of the adjustable coil or inductor is

R_{2}, and R_{3} are the resistance value of the other two resistive arms respectively.

From the above-shown expression of the balanced condition of an AC Bridge, we can write the balanced condition of Maxwell Bridge as follows

By equating real and imaginary parts of the equation separately, we get

So we have seen that we can calculate the value of unknown inductance (L_{1}) of the coil in terms of the known inductance of the variable inductor and resistances of others two arms.

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