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Measurement of Self-Inductance by Maxwell Bridge
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Objective:  In this bridge, an inductance is meaured by comparison with a standard variable capacitance. The connection shown in the figure.

 

 

Circuit Diagram:

 

                                                                                               

 

 L=Unknown Inductance ,

 

R4=effective resistance of unknown Inductance coil ,

 

R1,R2,R3= known non inductive resistance,

 

C1=Standard variable capacitor.

  

 Writing the equation  for  balance       

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«mo»(«/mo»«msub»«mi»R«/mi»«mn»4«/mn»«/msub»«mo»+«/mo»«mi»j«/mi»«mi»w«/mi»«mi»L«/mi»«mo»)«/mo»«mo»*«/mo»«mo»(«/mo»«mfrac»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«mrow»«mn»1«/mn»«mo»+«/mo»«mi»j«/mi»«mi»w«/mi»«msub»«mi»C«/mi»«mn»1«/mn»«/msub»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«/mrow»«/mfrac»«mo»)«/mo»«mo»=«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«mo»*«/mo»«msub»«mi»R«/mi»«mn»3«/mn»«/msub»«mo»;«/mo»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«mo»*«/mo»«msub»«mi»R«/mi»«mn»4«/mn»«/msub»«mo»+«/mo»«mi»j«/mi»«mi»w«/mi»«mi»L«/mi»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«mo»*«/mo»«msub»«mi»R«/mi»«mn»3«/mn»«/msub»«mo»+«/mo»«mi»j«/mi»«mi»w«/mi»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«msub»«mi»R«/mi»«mn»3«/mn»«/msub»«msub»«mi»C«/mi»«mn»1«/mn»«/msub»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«mo»;«/mo»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«/mtable»«/math»

Equating the real and imaginary parts , 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«msub»«mi»R«/mi»«mn»4«/mn»«/msub»«mo»=«/mo»«mfrac»«mrow»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«msub»«mi»R«/mi»«mn»3«/mn»«/msub»«/mrow»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«/mfrac»«mo»;«/mo»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mi»L«/mi»«mo»=«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«msub»«mi»R«/mi»«mn»3«/mn»«/msub»«msub»«mi»C«/mi»«mn»1«/mn»«/msub»«mo»§nbsp;«/mo»«mo»;«/mo»«/mtd»«/mtr»«/mtable»«/math»

Two variables R1 and C1 which appear in one of the two balance equations and hence the two equations are independent.

The expression for Q factor

                   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«mi»Q«/mi»«mo»=«/mo»«mfrac»«mrow»«mi»w«/mi»«mi»L«/mi»«/mrow»«msub»«mi»R«/mi»«mn»4«/mn»«/msub»«/mfrac»«mo»=«/mo»«mi»w«/mi»«msub»«mi»C«/mi»«mn»1«/mn»«/msub»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«/mtable»«/math»

 Phasor Diagram:

 

                                                     

                                                   

 

 

 

 

Cite this Simulator:

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