Instrumentation & Measurement Lab Experiments

Measurement of inductance using Maxwell’s Bridge

May 28 2023

Aim

To determine unknown inductance of a given coil by Maxwell’s Bridge method.

Apparatus Required:

S.No	Name	Type	Quantity
1	Maxwell’s Bridge training kit	EE-124	1
2	Patch cords	-	5-8
3	Multimeter	Digital	1
4	Audio oscillator		1

Introduction

Impedance at audio and radio frequency is communally determined by means of an AC bridge known as Wheatstone bridge the schematics diagram is as shown as figure. This bridge is similar to the DC bridge (Used for measuring resistances) except that instead of being regarded as simple resistances The arms are now impedances which may have reactive component also the bridge is exceeded by alternating current rather than direct current and the Galvanometer is replaced by means such that as headphone for detecting alternating currents An AC bridge is balanced when the two junction across whom the null detector is connected are at the same potential at same instant of the AC cycle the current flow through the detector is zero. This will happen when the AC potential across point ‘ab’ and ‘ad’ have the same magnitude and are in phase and also those across ‘bc’ and ‘dc’.

Theory

The Maxwell’s Bridge is an a.c bridge, which is extensively used for the measurement of unknown inductance. It uses different combination of resistor, capacitor & inductor. Here it is assumed that the capacitor is loss less and resistor are purely non inductive In this we are using headphone as a detector and at the balance condition the junction across the detector have same potential .So the detector works as null detector through which the value of current is zero.

Circuit Diagram

Proof:According to the explanation of the AC bridges the bridge is balanced when two junctions across whom the null detector is connected are at the same potential at all instants of the AC cycles. So the current through the detector is zero this can be expressed mathematically as follows:

E _ab= E _ad

Z₁I₁ = Z₄I₂................................................(1)

E _cb= E _ed

Z₂I₁ = Z₃I₂................................................(2)

Divide Eq [1] by Eq . [2]

Z₁I₁/Z₂I₁=Z₄I₂/Z₃I₂

Z₁Z₃ = Z₂Z₄................................................(3)

This is balance condition. Where Z₁, Z₂, Z₃ & Z₄, are the impedances of the arms respectively and are vector, Complex quantities.

Z₁, Z₃= Z₂, Z₄

Where

Z₁= R₁/1+jwC₁R₁

Z₂= R₂

Z₃= R_x+jwL_x

Z₄= R₄

Substituting these values in Eq. [3] we get.

R₁(R_x+jwL_x)/1+jwC₁R₁=R₂R₄

∴R₁R_x+jwL_xR_x=R₂R₄+jwC₁R₁R₂R₄

Separating the real & imaginary parts we get

R₁R_x =R₂R₄

or L_xR₁ =R₁R₂C₁R₄

L_x=R₂C₁R₄

Procedure:-

Select one of the unknown inductance L_x & connect on the appropriate place using two patch cords.
Select one of the standard capacitor C₁ using band switch.
Select 100 Ω value of R_x using band switch.
Connect headphone provided with this model at the place indicated.
Connect audio oscillator at the appropriate place indicated & switch it ON.
Now vary R₂ using Pot and select the value for no sound (null point) in the head phone.
It the null point does not detect for selected one value of C1 &RX, change the value of C₁&R_x now again varies R₂ using Pot and select the value for null point in the head phone.
Now switch OFF the supply and detach all patch chords.
Measure the resistances R_x&R₂ using multimeter and note down various values into the observation table.
Change the value or unknown inductance L_x using band switch & repeat all above steps.