Question

18 : If two coils having self-inductances L1 and L2 and a
mutual inductance Mare connected in series with
opposite polarity, then the total inductance of the
combination will be​

Answer 1

Given:

Self inductance of two coil is given as $L_1$ and $L_2$.

Mutual inductance is M

Coils are connected in series combination with opposite polarity.

To Find:

Total inductance of the given connection.

Solution:

The coils are connected with series combination and with opposite polarity, so,

Inductance e.m.f. in $L_1$ = $L_1\frac{di}{dt}+M\frac{di}{dt}$      .....(1)

And inductance e.m.f in $L_2$ = $L_2\frac{di}{dt}-M\frac{di}{dt}$   ......(2)  (-ve sign is due to opposite  

polarity)

Now, by adding both (1) and (2) we get the total inductance,

∴Total inductance e.m.f.  =  $L_1\frac{di}{dt}+L_2\frac{di}{dt} = (L_1+L_2)\frac{di}{dt}$    ......(3)

∴From the equation (3) we get the total inductance of the combination is $(L_1+L_2)$