# Owen’s Bridge

**Definition:** The **bridge** which **measures** the **inductance** in terms of **capacitance** is known as Owen’s bridge. It **works** on the** principle** of** comparison** i.e., the value of the **unknown inductor** is **compared** with the standard **capacitor**. The connection diagram of Owen’s bridge is shown in the figure.

The** ab, bc, cd** and **da** are the four arms of Owen’s bridge. The arms **ab** are purely inductive and the arm** bc** is purely resistive in nature. The arm **cd** has fixed capacitor and the arm **ad** consists the variable resistor and capacitor connected in series with the circuit.

The unknown inductor **L _{1} **of arm

**ab**is compared with the known capacitor

**C**connected to the arm

_{4}**cd**. The bridge is kept in balanced condition by independently varying the resistor

**R**and the capacitor

_{2}**C**. At the balanced condition, no current flows through the detector. The end points (b and c) of the detector are at the same potential.

_{2}## Phasor Diagram of Owen’s Bridge

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

The current **I _{1}, E_{3} = I_{3}R_{3 }and E_{4} = ωI_{2}C_{4}** are all on the same phases and are represented on the horizontal axis. The voltage drop

**I**in the arm

_{1}R_{1}**ab**is also represented on the horizontal axis.

The sum of the inductive voltage drop **ωL _{1}I_{1}** and the resistive voltage drop

**I**gives the voltage drop

_{1}R_{1}**E**of the arm

_{1}**ab**. When the bridge is in the balanced condition the potential

**E**and

_{1}**E**across the arm

_{2}**ab**and

**ad**are equal. Thus, it is shown on the same axis.

The voltage drop **V _{2}** is the summation of the resistive voltage drop

**I**and capacitive voltage drop

_{2}R_{2}**I**. The

_{2}/wC_{2}**I**of the arm

_{2}**a**

**d**lead by

**90º**with the voltage drop

**V**of the arm

_{4 }**cd**because of the fixed capacitor

**C**.

_{4}The current **I _{2} **and the voltage

**I**are represented on the vertical phases shown in the figure above. The supply voltage is obtained by adding the voltage

_{2}R_{2}**V**and

_{1}**V**.

_{3}## Theory of Owen’s Bridge

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

R_{2} – variable non-inductive resistance

R_{3} – fixed non-inductive resistance

C_{2} – variable standard capacitor

C_{4} – fixed standard capacitor

On separating the real and imaginary part we get,

### Advantages of Owen’s Bridge

The following are the advantages of Owen’s bridge.

- The balance equation is easily obtained.
- The balance equation is simple and does not contain any frequency component
- The bridge is used for the measurement of the large range inductance.

### Disadvantages of Owen’s Bridge

- The bridge uses an expensive capacitor which increases the cost of the bridge and also it gives a one percent accuracy.
- The value of the fixed capacitor C
_{2}is much larger than the quality factor Q_{2}

The Owen’s bridge is modified by connecting the voltmeter in parallel with the resistive arms of the bridge. The direct and alternating both the supply is given to the bridges. The ammeter is connected in series with the bridge for measuring the DC current. and the alternating current is measured by the help of voltmeter.