[![enter image description here](https://i.stack.imgur.com/5LJgt.png)](https://i.stack.imgur.com/5LJgt.png)

In the above diagram the circuit is in Series Resonance. Now we are asked to find the coupling coefficient K between coils L1 and L2. 
For which i first calculated L(equivalent) as follows :

```
Leq = L1 + L2 + 2M ( Dots are in aiding position)
Leq = 12 + 3 + 2M (Assuming w = 1)
Leq = 15 + 2M (M denotes mutual inductance between two coils)

```

So the circuit becomes

[![enter image description here](https://i.stack.imgur.com/Xr6XP.png)](https://i.stack.imgur.com/Xr6XP.png)

Since The circuit is in resonace the XL should equal to Xc

```
  Xc = XL
-jw18 = jw(15+2M)
 -18  = 15 + 2M ( w = 1)
  -16.5 = M

```

Now, To find coupling coefficient K, we can use the follow formula

```
K = M / sqrt(L1*L2)
K = -16.5/ sqrt(12*3) = -2.75

```

**Which is not possible, Since Range of k should be 0 < K < 1.**
Where am i wrong ? Please Help...