Measurement of self / mutual inductance and coupling coefficient of coils

AIM:

To measure self inductance of two coils, mutual inductance between these and the coefficient of coupling

APPARATUS REQUIRED:

AC Ammeter (0-2)A MI , Voltmeter (0-250)V  MI , 230/115 V Transformer, Autotransformer

THEORY:

When the two coils are connected for additive polarity the fluxes produced by the current in the two coils will aid each other and hence the impedance is high. This require the equivalent inductance to be very high. In this case, the mutual inductance terms will have the same sign as that of the self inductance terms. Thus, if the two coils having inductance L1 and L2 respectively and a mutual inductance of M between them are connected for additive polarity, the equivalent inductance

 La = L1 + L2 + 2M – (1)

 When the two coils are connected for subtractive polarity, the two fluxes will oppose each other and the inductance and hence the impedances are low. In this case the mutual inductance terms will have the opposite sign as that of the self inductance terms. Hence the equivalent inductance 

Ls = L1 + L2 – 2M – (2) 

From (1) and (2), we can find out M, L1 and L2. Thus the coefficient of coupling is calculated by the formula

K = M/√ L1 L2

PROCEDURE:

1. Connect the circuit as per the circuit diagram.
2. Keeping autotransformer at minimum position supply is switched ON.
3. Autotransformer is varied till voltmeter reach rated voltage.
4. Autotransformer is bought to minimum position and supply is switched off.

CIRCUIT DIAGRAM:

OBSERVATION:

Additive Polarity:

Substactive pol Polarity:

CALCULATIONS:

• L a= L1 + L2 + 2M ………….. (1)
• L s= L1 + L2 – 2M ………….. (2) 
• La – Ls = 4M
• :. M= (La – Ls)/4 …………….(3)
• La + Ls = 2 ( L1+ L2)
• :. ( L1+ L2) = (La + Ls)/ 2
• L1/L2 = N12/N22 = V12/V22…….(4)

From (1) (2)(3) & (4)  We will get the mutual inductance &self inductance of the coil.

Coupling Coefficient , K = M/ (√L1 L2)

RESULT :

• Self inductance of primary coil L1 = __________________ 
• Self inductance of primary coil L2 = __________________ 
• Mutual inductance M = __________________ 
• Coefficient of coupling K = __________________