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
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...