The Anderson bridge is a type of bridge circuit used to measure the unknown inductance of a coil. It is named after its inventor, Arthur Anderson. In this bridge circuit, the unknown inductance is measured in terms of known resistance and capacitance values.

**How does the Anderson bridge work?**

The Anderson bridge consists of four arms, each containing a combination of resistance and reactance (inductance or capacitance). The arms are connected in a bridge configuration, with a galvanometer connected between two junction points.

The bridge is balanced when the galvanometer shows zero deflection, indicating that the ratio of the resistances in the two arms is equal to the ratio of the reactances in the other two arms. At this balanced condition, the following relationship holds true:

R1/R2 = X3/X4

Where R1 and R2 are the resistances in two arms, and X3 and X4 are the reactances in the other two arms.

**Measuring the unknown inductance**

To measure the unknown inductance, one of the arms of the Anderson bridge is replaced with the unknown inductor. The other three arms contain known resistance and capacitance values.

When the bridge is balanced, the known resistance and capacitance values can be used to calculate the unknown inductance. The balance equation can be rearranged as follows:

R1/R2 = X3/X4

R1 = R2*(X3/X4)

Since the values of R1, R2, X3, and X4 are known, the unknown inductance can be determined by solving this equation.

**Why is the unknown inductance measured in terms of resistance and capacitance?**

The unknown inductance is measured in terms of resistance and capacitance because the bridge circuit relies on the relationship between the resistances and reactances to achieve balance. By using known resistance and capacitance values, the bridge circuit can be balanced, allowing the unknown inductance to be determined.

In option D, the correct answer, the unknown inductance is measured in terms of resistance and capacitance, which aligns with the principle of the Anderson bridge.

D