Mutual inductance and coefficient of coupling:

The equivalent inductance of two series connected coil (with mutual inductance among them) is 0.8 or 0.2 Henry based on the relative directions of currents in the coil. If self inductance of one coil is 0.4 Henry then find out (a) Mutual inductance; and (b) coefficient of coupling.

Solution

For M-Positive :

L_eq = L₁ + L₂ + 2M

0.8 = L₁ + L₂ + 2M        ---------------- (i)

Figure

For M negative

L_eq = L₁ + L₂ - 2M

0.2  = L₁ + L₂ - 2M       ----------- (ii)

 From Eqs. (i) and (ii)

0.6 = 4M ⇒ M =0.6/ 4 = 0.15 Henry

But       L₁ = 0.4 Henry

∴From Eq. (i)

0.8 = 0.4 + L₂  + 2 × 0.15

∴          L₂ = 0.1 Henry

 The coefficient of coupling