maxwell inductance bridge experiment pdf

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

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

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.

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.

Related terms:

• Wheatstone Bridge
• Anderson’s Bridge
• Owen’s Bridge
• Wien’s Bridge

2 thoughts on “Maxwell’s Bridge”

Very nicely explained

Very nice explained, I passed BE by your explanation.

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Measurement of inductance using Maxwell’s Bridge

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

Apparatus Required:

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’.

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

Z 1 I 1 = Z 4 I 2 ................................................(1)

E cb = E ed

Z 2 I 1 = Z 3 I 2 ................................................(2)

Divide Eq [1] by Eq . [2]

Z 1 I 1 /Z 2 I 1 =Z 4 I 2 /Z 3 I 2

Z 1 Z 3 = Z 2 Z 4 ................................................(3)

This is balance condition. Where Z 1 , Z 2 , Z 3 & Z 4 , are the impedances of the arms respectively and are vector, Complex quantities.

Z 1 , Z 3 = Z 2 , Z 4

Z 1 = R 1 /1+jwC 1 R 1

Z 3 = R x +jwL x

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

R 1 (R x +jwL x )/1+jwC 1 R 1 =R 2 R 4

∴R 1 R x +jwL x R x =R 2 R 4 +jwC 1 R 1 R 2 R 4

Separating the real & imaginary parts we get

R 1 R x =R 2 R 4

or L x R 1 =R 1 R 2 C 1 R 4

L x =R 2 C 1 R 4

Procedure:-

• Select one of the unknown inductance L x & connect on the appropriate place using two patch cords.
• Select one of the standard capacitor C 1 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 R 2 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 C 1 &R x now again varies R 2 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 &R 2 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.

Observation Table:

Selected value of R 1 ………..

Selected value of C 2 ……….

Selected value of R 4 ………..

Conclusion:- The value of unknown inductance L x has been calculated and when compared with standard values were found close to each other.

Viva-Voice Question:-

• Describe the detectors used for AC bridge
• What is the range of Q.?
• What is advantage of Maxwell Bridge?
• What is meant by Q factors of the coil?

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Maxwell's Inductance Bridge

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Chapter 5 Electrical circuit components

1- Resistance Electrical circuit components

2- Inductance

Fixed inductance Electrical circuit components

Variable inductance Electrical circuit components

3- Capacitance

Fixed capacitance Electrical circuit components

Variable capacitance Electrical circuit components

If we have an unknown resistance or inductance or capacitance, how can we accurately measure it???

The unknown resistance or inductance or capacitance sometimes represent a practical element such as: • Determination of short circuit location in telephone lines or power cables. • Determination of transformer winding inductance, capacitance and resistance. • etc. DC andAC Bridge can be considered the best choice. DC Bridges

1. DC bridges are the most accurate method for measuring resistances.

2. AC bridges are most popular, convenient and accurate instruments for measurement of unknown inductance, capacitance and some other related quantities. DC Bridges

Wheatstone bridge. DC Bridges

Introduction to AC Bridges

Alternating current bridges are most popular, convenient and accurate instruments for measurement of unknown inductance, capacitance and some other related quantities.

In its simplest form, ac bridges can be thought of to be derived from the conventional dc Wheatstone bridge. Introduction to AC Bridges

An ac bridge, in its basic form, consists of four arms, an alternating power supply, and a balance detector.

Balance is indicated by zero response of the detector. At balance, no current flows through the detector, i.e., there is no potential difference across the detector, or in other words, the potentials at points B and C are the same. Introduction to AC Bridges

An ac bridge, in its basic form, consists of four arms, an alternating power supply, and a balance detector. Introduction to AC Bridges

All AC bridges must have two variables to guarantee magnitude and phase balance Introduction to AC Bridges

Example Introduction to AC Bridges Introduction to AC Bridges Introduction to AC Bridges Introduction to AC Bridges Introduction to AC Bridges

Measurement of inductance Maxwell’s Inductance Bridge Hay’s Bridge Anderson’s Bridge Owen’s Bridge

Measurement of capacitance De Sauty’s Bridge Schering Bridge Wien’s Bridge Maxwell’s Inductance Bridge

This bridge is used to measure the value of an unknown inductance by comparing it with a variable standard self-inductance. Maxwell’s Inductance Bridge Simple analysis method Maxwell’s Inductance Bridge Simple analysis method Maxwell’s Inductance Bridge Detailed analysis method

This bridge is used to measure the value of an unknown inductance by comparing it with a variable standard self-inductance. Maxwell’s Inductance Bridge

Bridge description

The unknown inductor L1 of resistance R1 in the branch AB is compared with the standard known inductor L2 of resistance R2 on arm AC.

Branch BD and CD contain known non-inductive resistors R3 and R4 respectively. Maxwell’s Inductance Bridge

Balance requirement

The bridge is balanced by varying L2 and one of the resistors R3 or R4. Alternatively, varying R3 (for magnitude balance) and R2 (for phase balance). Maxwell’s Inductance Bridge

Under balance condition

Under balance condition, currents in the arms AB and BD are equal

(I1). Similarly, currents in the arms AC and CD are equal (I2).

Under balanced condition, since nodes B and D are at the same potential, voltage drops across arm BD and CD are equal (V3 = V4); similarly, voltage drop across arms AB and AC are equal (V1 = V2). Maxwell’s Inductance Bridge

As shown in the phasor diagram, V3 and V4 being equal, they are overlapping. Arms BD and CD being purely resistive, currents through these arms will be in the same phase and in phase with the voltage drops across these two respective branches. Thus, currents I1 and I2 will be collinear with the phasors V3 and V4. Maxwell’s Inductance Bridge

The same current I1 flows through branch AB as well, thus the voltage drop I1R1 remains in the same phase as I1. Voltage drop wL1I1 in the inductor L1 will be 90° out of phase (Leading) with I1R1. Phasor summation of these two voltage drops I1R1 and wL1I1 will give the voltage drop V1 across the arm AB.

The voltage across the two branches AB and AC are equal, thus the two voltage drops V1 and V2 are equal and are in the same phase. Finally, phasor summation of V1 and V3 (or V2 and V4) results in the supply voltage V Maxwell’s Inductance Bridge

V = V V V 1 2 1 = 2 V3 = V4 V3 V4 Maxwell’s Inductance Bridge Maxwell’s Inductance Bridge Maxwell’s Inductance–Capacitance Bridge Maxwell’s- Wien Bridge In this bridge, the unknown inductance is measured by comparison with a standard variable capacitance. It is much easier to obtain standard values of variable capacitors with acceptable degree of accuracy. This is however, not the case with finding accurate and stable standard value variable inductor as is required in the basic Maxwell’s bridge Maxwell’s Inductance–Capacitance Bridge Maxwell’s-Wien Bridge Simple analysis method Maxwell’s Inductance–Capacitance Bridge Maxwell’s-Wien Bridge Simple analysis method Maxwell’s Inductance–Capacitance Bridge Maxwell’s Wien Bridge Detailed analysis method

Basic Maxwell’s bridge Maxwell’s Wien Bridge Maxwell’s Inductance–Capacitance Bridge Maxwell’s Wien Bridge

The unknown inductor L1 of effective resistance R1 in the branch AB is compared with the standard known variable capacitor C4 on arm CD. The other resistances R2, R3, and R4 are known as non– inductive resistors. Maxwell’s Inductance–Capacitance Bridge Maxwell’s Wien Bridge

The bridge is preferably balanced by varying C4 and R4, giving independent adjustment settings. Maxwell’s Inductance–Capacitance Bridge Maxwell’s Wien Bridge

Under balanced condition, no current flows through the detector. Under such condition, currents in the arms AB and BD are equal (I1). Similarly, currents in the arms AC and CD are equal (I2). Under balanced condition, since nodes B and D are at the same potential, voltage drops across arm BD and CD are equal (V3 = V4); similarly, voltage drops across arms AB and AC are equal (V1 = V2). Maxwell’s Inductance–Capacitance Bridge Maxwell’s Wien Bridge

As shown in the phasor diagram of, V3 and V4 being equal, they are overlapping both in magnitude and phase. The arm BD being purely resistive, current I1through this arm will be in the same phase with the voltage drop V3 across it. Similarly, the voltage drop V4 across the arm CD, current IR through the resistance R4 in the same branch, and the resulting resistive voltage drop IRR4 are all in the same phase Maxwell’s Inductance–Capacitance Bridge Maxwell’s Wien Bridge

The resistive current IR when added with the quadrature capacitive current IC, results in the main current I2 flowing in the arm CD. This current I2 while flowing through the resistance R2 in the arm AC, produces a voltage drop V2 = I2R2, that is in same phase as I2. Under balanced condition, voltage drops across arms AB and AC are equal, i.e., V1 = V2. This voltage drop across the arm AB is actually the phasor summation of voltage drop I1R1 across the resistance R1 and the quadrature voltage drop wL1I1 across the unknown inductor L1. Finally, phasor summation of V1 and V3 (or V2 and V4) results in the supply voltage V. Maxwell’s Inductance–Capacitance Bridge Maxwell’s Wien Bridge

Under balance condition Maxwell’s Inductance–Capacitance Bridge Maxwell’s Wien Bridge Maxwell’s Inductance–Capacitance Bridge Maxwell’s Wien Bridge

Advantages of Maxwell’s Bridge 1. The balance equations are independent of each other, thus the two variables

C4 and R4 can be varied independently. 2. Final balance equations are independent of frequency. 3. The unknown quantities can be denoted by simple expressions involving known quantities. 4. Balance equation is independent of losses associated with the inductor. 5. A wide range of inductance at power and audio frequencies can be measured. Maxwell’s Inductance–Capacitance Bridge Maxwell’s Wien Bridge

Disadvantages of Maxwell’s Bridge 1. The bridge, for its operation, requires a standard variable capacitor, which can be very expensive if high accuracies are asked. In such a case, fixed

value capacitors are used and balance is achieved by varying R4 and R2. 2. This bridge is limited to measurement of low Q inductors (1< Q < 10). 3. Maxwell’s bridge is also unsuited for coils with very low value of Q (e.g., Q < 1). Such low Q inductors can be found in inductive resistors and RF coils. Maxwell’s bridge finds difficult and laborious to obtain balance while measuring such low Q inductors. Anderson’s Bridge Simple analysis method

D B E E E A A A Anderson’s Bridge B C B

D B E E E A A A Maxwell’s Wien Bridge

Anderson’s Bridge Anderson’s Bridge (1) Anderson’s Bridge Detailed analysis method This method is a modification of Maxwell’s inductance–capacitance bridge, in which value of the unknown inductor is expressed in terms of a standard known capacitor. This method is applicable for precise measurement of inductances over a wide range of values.

Bridge description Anderson’s Bridge

The unknown inductor L1 of effective resistance R1 in the branch AB is compared with the standard known capacitor C on arm ED. The bridge is balanced by varying r. Anderson’s Bridge

Under balanced condition, since no current flows through the detector, nodes B and E are at the same potential. Anderson’s Bridge

As shown in the phasor diagram, I1 and V3 = I1R3 are in the same phase along the horizontal axis. Since under balance condition, voltage drops across arms

BD and ED are equal, V3 = I1R3 = IC/wC and all the three phasors are in the same phase. Anderson’s Bridge

The same current I1, when flowing through the arm AB produces a voltage drop I1(R1 + r1) which is once again, in phase with I1. Since under balanced condition, no current flows through the detector, the same current IC flows through the resistance r in arm CE and then through the capacitor C in the arm ED. Anderson’s Bridge

Phasor summation of the voltage drops ICr in arm the CE and IC /wC in the arm ED will be equal to the voltage drop V4 across the arm CD. V4 being the voltage drop in the resistance R4 on the arm CD, the current I4 and V4 will be in the same phase. Anderson’s Bridge

As can be seen from the Anderson’s bridge circuit , and also plotted in the phasor diagram, phasor summation of the currents I4 in the arm CD and the current IC in the arm CE will give rise to the current I2 in the arm AC. This current I2, while passing through the resistance R2 will give rise to a voltage drop V2 = I2R2 across the arm AC that is in phase with the current I2. Anderson’s Bridge

Since, under balance, potentials at nodes B and E are the same, voltage drops between nodes A -B and between A -C -E will be equal.

Thus, phasor summation of the voltage drop V2 = I2R2 in the arm AC and ICr in arm the CE will build up to the voltage V1 across the arm AB. The voltage V1 can also be obtained by adding the resistive voltage drop I1(R1 + r1) with the quadrature inductive voltage drop wL1I1 in the arm AB. Anderson’s Bridge

At balance, VBD = VED Anderson’s Bridge

Under balance condition Anderson’s Bridge

Advantages and dis advantages

The advantage of Anderson’s bridge over Maxwell’s bride is that in this case a fixed value capacitor is used thereby greatly reducing the cost. This however, is at the expense of connection complexities and balance equations becoming tedious.

Hay’s Bridge

Hay’s bridge is a modification of Maxwell’s bridge. This method of measurement is particularly suited for high Q inductors (L>>>R) Hay’s Bridge Simple analysis method Hay’s Bridge Simple analysis method Hay’s Bridge Detailed analysis method

Hay’s bridge is a modification of Maxwell’s bridge. This method of measurement is particularly suited for high Q inductors (L>>>R)

Bridge description Hay’s Bridge

The unknown inductor L1 of effective resistance R1 in the branch AB is compared with the standard known variable capacitor C4 on arm CD. This bridge uses a resistance R4 in series with the standard capacitor C4 (unlike in Maxwell’s bride where R4 was in parallel with C4). The other resistances R2 and R3 are known no-inductive resistors. The bridge is balanced by varying C4 and R4 or varying R4 and R2 Hay’s Bridge

Under balanced condition, since no current flows through the detector, nodes B and D are at the same potential, voltage drops across arm BD and CD are equal

(V3 = V4); similarly, voltage drops across arms AB and AC are equal (V1 = V2). Hay’s Bridge

As shown in the phasor diagram, V3 and V4 being equal, they are overlapping both in magnitude and phase and are draw on along the horizontal axis. The arm BD being purely resistive, current I1 through this arm will be in the same phase with the voltage drop V3 = I1R3 across it. The same current I1, while passing through the resistance R1 in the arm AB, produces a voltage drop I1R1 that is once again, in the same phase as I1. Total voltage drop V1 across the arm AB is obtained by adding the two quadrature phasors I1R1 and wL1I1 representing resistive and inductive voltage drops in the same branch AB. Hay’s Bridge

Since under balance condition, voltage drops across arms AB and AC are equal, i.e., (V1 = V2), the two voltages V1 and V2 are overlapping both in magnitude and phase. The branch AC being purely resistive, the branch current I2 and branch voltage V2 will be in the same phase. voltage V. Hay’s Bridge

The same current I2 flows through the arm CD and produces a voltage drop I2R4 across the resistance R4. This resistive voltage drop I2R4, obviously is in the same phase as I2. The capacitive voltage drop I2/wC4 in the capacitance C4 present in the same arm AC will however, lag the current I2 by 90°. Phasor summation of these two series voltage drops across R4 and C4 will give the total voltage drop V4 across the arm CD. Finally, phasor summation of V1 and V3 (or V2 and V4) results in the supply voltage V. Hay’s Bridge

Under balance condition Hay’s Bridge

The bridge is frequency dependent Hay’s Bridge Hay’s Bridge Owen’s Bridge Owen’s Bridge Simple analysis method Owen’s Bridge Detailed analysis method This bridge is used for measurement of unknown inductance in terms of known value capacitance. This bridge has the advantages of being useful over a very wide range of inductances with capacitors of reasonable dimension.

Bridge description Owen’s Bridge

The unknown inductor L1 of effective resistance R1 in the branch AB is compared with the standard known capacitor C2 on arm AC. The bridge is balanced by varying R2 and C2 independently Owen’s Bridge

Prove and verify with the aid of phasor diagram Owen’s Bridge Owen’s Bridge

• Wheatstone_bridge
• Galvanometer
• Maxwell_bridge
• Bridge_circuit
• Carey_Foster_bridge
• Kelvin_bridge
• Universal_motor

Measurement Of Self Inductance By Maxwell’s Bridge

Maxwell’s Bridge, named after the renowned physicist James Clerk Maxwell, is a type of bridge circuit used for measuring unknown electrical parameters. It is specifically designed for measuring self-inductance and mutual inductance. The bridge is constructed using resistors, capacitors, and inductors, and it operates based on the principle of balanced bridge circuits, where the ratio of two impedances is compared.

The main idea behind Maxwell’s Bridge is to balance the bridge circuit by adjusting known components until there is no current flowing through the galvanometer. This balanced condition indicates that the ratio of the impedances in the arms of the bridge is equal, allowing for the calculation of the unknown parameter – in this case, self-inductance.

The Components of Maxwell’s Bridge

Maxwell’s Bridge consists of four arms, each containing different combinations of resistors, capacitors, and inductors. The bridge arms are labeled P, Q, R, and S. The basic configuration of the bridge is as follows:

• Arm P: Consists of a resistor R 1​ and an inductor L 1​.
• Arm Q: Contains a resistor R 2​ and an inductor L 2​.
• Arm R: Comprises an inductor L x ​ (whose self-inductance is to be measured) and a resistor R x ​.
• Arm S: Contains a capacitor C .

A galvanometer is connected between point A and point B, which helps us determine when the bridge is in a balanced condition. The goal is to adjust the values of resistors, capacitors, and inductors in arms P, Q, and R until the bridge is balanced, and no current flows through the galvanometer.

The Principle of Balancing the Bridge

The key principle of Maxwell’s Bridge lies in achieving a balanced condition, which is obtained when the impedances of the two halves of the bridge are equal. In mathematical terms, this can be expressed as:

Zp * Zs = Zq * Zr

• Zp and ​Zs are the impedances of arms p and q, respectively.
• Zq​ and Zr​ are the impedances of arms r and s, respectively.

To determine self-inductance using Maxwell’s Bridge, we rearrange the equation as follows:

Z ​p/Zq=​ Zr /Zs​​

Since the impedances are complex quantities involving both magnitude and phase, it’s essential to balance the bridge for both real and imaginary components. This requires adjusting the values of resistors, capacitors, and inductors in arms P, Q, and R until the bridge is in equilibrium.

Procedure for Measuring Self-Inductance:

The process of measuring self-inductance using Maxwell’s Bridge involves several steps:

• Initial Setup: Connect the components as per the bridge diagram, with an unknown inductor in arm R and a capacitor in arm S.
• Balancing the Real Component: Adjust the values of resistors in arms P and Q to balance the bridge for the real component of impedance. This is done by comparing the voltage across points A and B using a galvanometer. Achieving a balanced condition indicates that the real components of impedances are equal.
• Balancing the Imaginary Component: After achieving balance for the real component, adjust the capacitor in arm S to balance the bridge for the imaginary component of impedance. This ensures that both the real and imaginary components of impedances are equal.
• Calculating Self-Inductance: Once the bridge is balanced, the ratios of impedances on both sides of the bridge are equal. Using the known values of resistors, capacitors, and the bridge equation, the self-inductance of the unknown inductor L x ​ can be calculated.

Maxwell’s inductance Bridge  circuit measures an inductance by comparison with a variable standard self-inductance. The connections and the phasor diagrams for balance conditions are shown in the  Maxwell’s Inductance Bridge   figure.

     L 1 = unknown inductance of resistance R 1

     L 2 = variable inductance of fixed resistance r 2

     R 2 = variable resistance connected in series with inductor L 2

 R 3 ,R 4 = known non-inductive resistances

         The theory of  Maxwell’s Inductance Bridge  has been explained already in ac bridges post.

              Resistors R 3 and R 4 are normally a selection of values from 10, 100, 1000 and 10,000 r 2 is a decade resistance box. In some cases, an additional known resistance may have to be inserted in series with the unknown coil in order to obtain balance.

Measurement Of Self Inductance By Maxwell’s Inductance Capacitance Bridge :  

            In  Maxwell’s Inductance Capacitance Bridge , an inductance  is measured by comparison. with a standard variable  capacitance. The connections and the phasor diagram  at the balance conditions are given in  Maxwell’s Inductance Capacitance Bridg e figure below .

Let                     L1 = unknown inductance,

                         R 1 = effective resistance of inductor L 1 ,

               R 2 , R 3 , R 4 = known non-inductive resistances,

            and       C 4 = variable standard capacitor.

       Thus we have two variables R 4 and C 4 which  appear in one of the two balance equations and hence  the two equations are independent.

The expression for Q factor,

                                  Q = ωL₁/R₁ = ωC₄R₄

Advantages of Maxwell’s Inductance Capacitance Bridge:

The advantages of  Maxwell’s Inductance Capacitance Bridge are

1.The two balance equations are independent  if we choose R4 and C 4 as variable elements.

2.The frequency does not appear in any of the  two equations.

3. Maxwell’s Inductance Capacitance Bridg e yields a simple expression for  unknowns L 1 and R 1 in terms of known  bridge elements.

       Physically R 2 and R 3 are each, say, 10, 100, 1000 or 10,000 Q and their value is selected to  give suitable value of product R 2 R 3 which  appears in both the balance equations; C 4 is  decade capacitor and R 4 a decade resistor.

        The simplicity of the bridge can be appreciated by the following example. Suppose the product R 2 R 3 is 10⁶.Therefore, inductance is L 1 = C4 x 10⁶. Thus when the balance is achieved the value of C 4 in μF directly gives the value of inductance in H. 

4.The Maxwell’s inductance capacitance bridge is very useful for measurement of a wide range of inductance at the power and audio frequencies. 

Disadvantages  of  Maxwell’s Inductance Capacitance Bridge:  

The main disadvantages of Maxwell’s inductance capacitance bridge are 

1. Maxwell’s Inductance Capacitance Bridge  requires a variable standard capacitor which may be very expensive if calibrated to a high degree of accuracy. Therefore sometimes a fixed standard capacitor is used, either because a variable capacitor is not available or because fixed capacitors have a higher degree of accuracy and are  less expensive than the variable ones. The balance adjustments are then done by 

           (a) either varying R 2 and R 4 and since R 2 appears in both the balance equations, the balance adjustments become difficult

          (b) putting an additional resistance in series with the inductance under measurement and then varying this resistance and R 4 . 

2.The bridge is limited to measurement of low Q coils, (1 < Q < 10). It is clear that the measurement of high Q coils demands a large value for resistance R 4 , perhaps 10⁵ or 10⁶. The resistance boxes of such high values are very expensive. Thus for values of Q > 10, Maxwell’s bridge is unsuitable.

            The Maxwell’s bridge is also unsuited for coils with a very low value of Q (i.e., Q < 1). Q values of this magnitude occur in inductive resistors, or in an R.F. coil if measured at low frequencies. The difficulty in measurement occurs on account of labour involved in obtaining b alance since nominally a fixed capacitor is used and balance is obtained by manipulating resistances R 2 and R 4 alternately.This difficulty is explained as below:

           A preliminary inductive balance is made with R 2 and then R 4 is varied to give a resistive balance which is dependent on the R 2 setting. Accordingly, when R 2 is changed for a second inductive balance, the resistive balance is disturbed and moves to a new value giving slow “convergence” to balance. This is particularly true of a low Q coil, for which resistance is prominent (as = wL/ R).

         Thus a sliding balance condition prevails and it takes many manipulations to achieve balance for low Q coils with Maxwell’s bridge . From the above discussions, we conclude that Maxwell’s bridg e is suited for measurements of only medium Q coils.

Conclusion:

          In this, we have learnt Measurement Of Self Inductance By Maxwell’s Inductance & Maxwell’s Capacitance Bridge . You can download this article as pdf, ppt.

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Determination of Inductance through Capacitance using Commercial LCR Meters

• Original Paper
• Published: 30 April 2021
• Volume 36 , pages 349–353, ( 2021 )

Cite this article

• Priyanka Jain   ORCID: orcid.org/0000-0002-3001-197X 1 , 2 ,
• Sachin Kumar 2 ,
• Jyotsana Mandal 2 ,
• Nidhi Singh 1 , 2 ,
• J. C. Biswas 2 &
• A. K. Saxena 2  

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Present work can be used to calibrate inductance standards by utilizing the error evaluated at the same nominal value of reactance of a capacitance standard. Inductance can be determined in terms of capacitance standard by direct measurement of capacitive reactance on the LCR meter. The conventional Maxwell–Wien bridge is currently used at CSIR-NPL to determine traceability to the inductance standard through capacitance and two resistance standards. However, proposed technique defines inductance in terms of one capacitance only. Measurement results of 100 mH inductors at 1 kHz are evaluated and validated with the inductor's previously assigned values with Maxwell–Wien bridge. Preliminary results obtained from both techniques were found within 50 ppm; hence this technique can be used as an alternative to Maxwell–Wien bridge.

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Acknowledgment

The authors would like to thank Director CSIR-NPL, Dr. D K Aswal, for his constant support and encouragement to carry out this work.

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Academy of Scientific and Innovative Research AcSIR), Ghaziabad, 201002, India

Priyanka Jain & Nidhi Singh

CSIR-National Physical Laboratory, New Delhi, 110012, India

Priyanka Jain, Sachin Kumar,  Satish, Jyotsana Mandal, Nidhi Singh, J. C. Biswas & A. K. Saxena

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Jain, P., Kumar, S., Satish et al. Determination of Inductance through Capacitance using Commercial LCR Meters. MAPAN 36 , 349–353 (2021). https://doi.org/10.1007/s12647-021-00444-2

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Received : 11 March 2021

Accepted : 26 March 2021

Published : 30 April 2021

Issue Date : June 2021

DOI : https://doi.org/10.1007/s12647-021-00444-2

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