INTRODUCTION Different types of AC Bridges can be used for measurement of either inductance or capacitance. We can measure unknown inductance by using MAXWELL’S INDUCTANCE BRIDGE. CONSTRUCTION: There are four different arms in which: First arm of the bridge contains series combination of resistance and inductance. Third arm consists of series combination of variable resistance and variable inductance. Second and fourth arm consists of resistances respectively.
WORKING OF THE BRIDGE • This coil is connected to AC supply when alternating current flows through the coil according to magnetic effect , it produces magnetic flux lines. • When these magnetic flux lines are cut by coil1 then according to FARADAY’s LAW of ELECTROMAGNETIC INDUCTION emf is induced in coil1.This emf is called as SELF INDUCED emf ,denoted by E1. • Mathematically E1=-L1(di/dt),where L is called as ‘SELF INDUCTANCE OF COIL’.
WORKING OF BRIDGE (CONTINUED) • Similarly in this figure there are 2 different coils in which coil1 is connected to AC supply and coil2 gets open. • When AC supply is given then according to the magnetic effect, magnetic flux lines are produced but some of the magnetic lines cut by coil2and all the magnetic lines cut by coil1. • Hence according to FARADAY’S LAW emf will be induced in both the coils. • • The emf induced in coil1 is called as SELF INDUCED EMF and the emf induced in coil2 is called as MUTUALLY INDUCED EMF. • Using MAXWELL’S INDUCTANCE BRIDGE we can measure only SELF INDUCTANCE of coil1.
DERIVATION In adjacent figure , parameters L1 and R1 are unknown parameters. By using MAXWELL’S INDUCTANCE BRIDGE we have to find out these parameters
DERIVATIONThe mathematical balancingcondition of AC bridge is: Z1.Z4=Z2.Z3-----(1)Where,Z1=(R1+jωL1)Z2=R2Z3=(R3+jωL3+r3)Z4=R4Substitute the values in eq.(1) R1R4+jωL1R4=R2(R3+r3)+jωL3R2
FINAL EQUATION Real part--- R1R4=R2(R3+r3) Imaginary part---L1R4=L3R2From these equations :The above 2 equations are FREE FROM FREQUENCY ie the values ofunknown resistance and unknown inductance does not depend upon thefrequency of supply. So that ANY TYPE OF DETECTOR can be used