# Maxwell’s Bridge

**Definition:** The **bridge** used for the** measurement** of **self-inductance** of the** circuit** is known as the Maxwell bridge. It is the advanced form of the Wheatstone bridge. The Maxwell bridge **works** on the **principle** of the **comparison**, i.e., the value of **unknown** **inductance** is determined by **comparing** it with the known value or standard value.

## Types of Maxwell’s Bridge

Two methods are used for determining the self-inductance of the circuit. They are

- Maxwell’s Inductance Bridge
- Maxwell’s inductance Capacitance Bridge

### Maxwell’s Inductance Bridge

In such type of bridges, the value of unknown resistance is determined by comparing it with the known value of the standard self-inductance. The connection diagram for the balance Maxwell bridge is shown in the figure below.

Let, L_{1} – unknown inductance of resistance R_{1}.

L_{2} – Variable inductance of fixed resistance r_{1}.

R_{2} – variable resistance connected in series with inductor L_{2}.

R_{3}, R_{4} – known non-inductance resistance

The value of the R_{3} and the R_{4} resistance varies from 10 to 1000 ohms with the help of the resistance box. Sometimes for balancing the bridge, the additional resistance is also inserted into the circuit.

The phasor diagram of Maxwell’s inductance bridge is shown in the figure below.

### Maxwell’s Inductance Capacitance Bridge

In this type of bridges, the unknown resistance is measured with the help of the standard variable capacitance. The connection diagram of the Maxwell Bridge is shown in the figure below.

Let, L_{1} – unknown inductance of resistance R_{1}.

R_{1} – Variable inductance of fixed resistance r_{1}.

R_{2}, R_{3}, R_{4} – variable resistance connected in series with inductor L_{2}.

C_{4} – known non-inductance resistance

By separating the real and imaginary equation we get,

The above equation shows that the bridges have two variables R_{4} and C_{4} which appear in one of the two equations and hence both the equations are independent.

The circuit quality factor is expressed as

Phasor diagram of Maxwell’s inductance capacitance bridge is shown in the figure below.

### Advantages of the Maxwell’s Bridges

The following are the advantages of the Maxwell bridges

- The balance equation of the circuit is free from frequency.
- Both the balance equations are independent of each other.
- The Maxwell’s inductor capacitance bridge is used for the measurement of the high range inductance.

### Disadvantages of the Maxwell’s Bridge

The main disadvantages of the bridges are

- The Maxwell inductor capacitance bridge requires a variable capacitor which is very expensive. Thus, sometimes the standard variable capacitor is used in the bridges.
- The bridge is only used for the measurement of medium quality coils.

Because of the following disadvantages, the Hays bridge is used for the measurement of circuit inductance which is the advanced form of the Maxwell’s Bridge.