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 L₁ of arm ab is compared with the known capacitor C₄ connected to the arm cd. The bridge is kept in balanced condition by independently varying the resistor R₂ and the capacitor C₂. At the balanced condition, no current flows through the detector. The end points (b and c) of the detector are at the same potential.

Phasor Diagram of Owen’s Bridge

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

The current I₁, E₃ = I₃R₃ and E₄ = ωI₂C₄ are all on the same phases and are represented on the horizontal axis. The voltage drop I₁R₁ in the arm ab is also represented on the horizontal axis.

The sum of the inductive voltage drop ωL₁I₁ and the resistive voltage drop I₁R₁ gives the voltage drop E₁ of the arm ab. When the bridge is in the balanced condition the potential E₁ and E₂ across the arm ab and ad are equal. Thus, it is shown on the same axis.

The voltage drop V₂ is the summation of the resistive voltage drop I₂R₂ and capacitive voltage drop I₂/wC₂. The I₂ of the arm ad lead by 90º with the voltage drop V₄  of the arm cd because of the fixed capacitor C₄.

The current I₂ and the voltage I₂R₂ are represented on the vertical phases shown in the figure above. The supply voltage is obtained by adding the voltage V₁ and V₃.

Theory of Owen’s Bridge

Let, L₁ – unknown self-inductance of resistance R₁
R₂ – variable non-inductive resistance
R₃ – fixed non-inductive resistance
C₂ – variable standard capacitor
C₄ – fixed standard capacitor

At balance condition, 

On separating the real and imaginary part we get,

And, 

Advantages of Owen’s Bridge

The following are the advantages of Owen’s bridge.

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

Disadvantages of Owen’s Bridge

1. The bridge uses an expensive capacitor which increases the cost of the bridge and also it gives a one percent accuracy.
2. The value of the fixed capacitor C₂ is much larger than the quality factor Q₂

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.