Concept of MUTUAL INDUCTUNCE and MAGNETIC COUPLING

• Definition of Mutual Induced emf:-

➝ " It is defined as the emf is induced in the coil due to the rate of change of flux is occurs in the nearest coil which is linked with it".

• EXPLANATION:-

Fig.(a) MUTUAL INDUCED VOLTAGE

Whre; 

             N1 = Numbers of turns of Coil A

             N2 = Numbers of turns of Coil B

             R.   = Variable Resistor

              G.  = Galvanometer

         Φ12. = Flux of coil A is linked with Coil B

         Φ21 = Flux of Coil B is linked with Coil A

➝ When supply voltage V is connected across Coil A then current I1 is flows through the coil A due to this current flux Φ1 is produced in the coil A, the direction of this flux Φ1 is found by RIGHT HAND CURL RULE as discussed in previous article.

➝ According to RIGHT HAND CURL RULE if the direction of current is in the direction of Curl then right hand thumb will represent the direction of magnetic field as shown in below figure.

➝ Some portion of this flux Φ1 is called as Φ12 is linked with Nearest Coil B, Now if we change the current I1 by changing the value of Variable Resistor R then flux Φ12 which is linked with Coil B is also change and due to this rate of change of Flux in Coil A, EMF is induced in nearest coil B and vice varsa. The direction of induced EMF in Coil B is found by RIGHT HAND CURL RULE.

• What is MUTUAL INDUCTUNCE?

⇨Mutual inductance is the property of the coil which Oppose the change of current in nearest coil.

                   M12 = N2 × Φ12/ I1 ...............(1)

                 M21 = N1 × Φ21 / I2 .............(2)

Now,. Suppose M12 = M21 = M

• Coefficient of Coupling (K):-

➝"Coefficient of Coupling K is describe the capability of flux linkages" OR it is defined as the fraction of the total flux that links with the Coil.

                 i.e.   K = Φ12/ Φ1 = Φ21/ Φ2 .......(3)

• Multiply equation number (1)&(2) with equation number (3) ..............

  M^2 = N1 × N2 × Φ12×Φ21/ I1×I2  × Φ1Φ2/ Φ1Φ2 .............(4)

• Rearrange term in above equation.......

    = N1Φ1/ I1 × N2Φ2/I2 × Φ12/ Φ1 × Φ21/Φ2 

     =  L1 × L2 × K × K 

• NOTE:- 

           L1 = N1Φ1/ I1

           L2 = N2Φ2/I2

             K = Φ12/ Φ1

             K = Φ21/Φ2

        ∴ M^2 = L1 × L2 × K^2

              M = K × √L1×L2 ...........(5)

        ∴ K = M/ √L1×L2 .............(6)

        ............Thank you 🙂.............