Owen’s bridge and measurement of increment inductance Effect On Induced Voltage. Measurements Of Incremental Inductance Diagram Of Increment Inductance. Description Of Ø-i Magnetizing Curve

1.  Topic: owen’s bridge and measurement of increment
inductance.

2. Owen’s bridge:

3. parameters of bridge :
L1 = unknown inductance having its resistance R1
R2 = variable non inductive resistance
R3 = fixed non inductive resistance
C2 = variable standard capacitor
C4 = fixed standard capacitor

4. Use of own’s bridge
 The own’s bridge use for the measurement of inductance is
expressed in the terms of capacitance

5. For A.C. bridges the balancing
condition for bridge is
Z1 Z4 = Z2 Z3
Z1 = ( R1 + jω L1 )
Z2 = R2 +
Z3 = R3
Z4 =

6. Z1 Z4 = Z2 Z3
comparing real terms;

7. Comparing imaginary terms

8. Phasor diagram:

9. Measurements Of Incremental Inductance
 The magnetic flux linking an ion-cored coil is not in direct
proportion to the current flowing in the coil, but varies in
manner usually indicated by a magnetization curve. The flux
usually increases fairly rapidly when the current build-up
process first begins.
 The flux increment to a particular size of current increment
becomes smaller with continual increase of current as the core
approaches saturation.

10.  An induced voltage in the coil depends on a change of flux and
hence becomes smaller for a given current change at higher
values of current.
 The basic expression for induced voltage in terms of a
changing flux is usually replaced by the coefficient of self
inductance multiplied by the rate of change of current.
Effect On Induced Voltage.

11. In terms of a flux change, the induced voltage is
ℓ= -Ndф/dt.
In terms of inductance,
ℓ= -Ldi/dt
where; L= coefficient of self inductance.
Comparison of the two expressions gives
L=Ndф/di
Which helps to explain the nature of this quantity. Inductance may
be repesented by the slope of the ф-i magnetization curve of a
reactor.

12.  For an air-cored coil there is a linear relationship between flux and
current hence L is a constant.
 For an iron-cored coil there is no linear flux-current relationship
hence L has different values depending on the portion of
magnetization curve being used and on the manner of defining L.
 Many iron cored coils are used as filter reactors in rectifier circuits
and in other applications.
Description Of Ø-i Magnetizing Curve

13.  The incremental inductance at this point may be defined a
square of turns multiply the slope of the ф-i curve.
Therefore, Incremental inductance
L= N² dф/di
 Similarly incremental permeability may be defined as the slope
of the B-H curve at the operating point.
Therefore, Incremental permeability
μ = dB/dH

14. The figure shows the Owen’s bridge for Measurement of
Incremental Inductance.
The incremental inductance can be measured with an Owen’s
Bridge. The original circuit, however, has to be modified in
order that the coil under measurement is fed from both dc and
ac.

15. Diagram Of Increment Inductance.

16. • The coil is fed from ac and dc sources in parallel. A blocking
capacitor C, is used to block direct current from entering the ac
source.
• A high inductance L, is used to block alternating current to
enter dc source. Any direct current must not affect the balance
and this condition is automatically satisfied in owen’s bridge
because capacitors C2 and C4 block any dc current flowing
through the detector.

17.  Dc component of current is measured by a moving coil
ammeter A connected in the dc supply circuit.
 Ac component of current can be obtained from the reading of a
valve voltmeter connected across R3.
 The value of current calculated from this readind is ac current
through R3, but this is also the ac current through the coil at
balance.

18. At balance, incremental inductance
L1 = N²/(l/μA)
μ= L1l/N²A
Where; N= number of turns
l= length of flux path
A= area of flux path
L1=incremental inductance

19. Thank you