1. In a two-coil system, the self-inductances $L_1 = L_2 = 4$ H. Suppose a voltage input across coil #1 is $v_1 = 16 \sin(120\pi t)$ V., and coil #2 is open with an induced voltage $v_2 = 8 \sin(120\pi t)$ V.
(a) Determine the coupling coefficient $k$ of the two coils;
(b) If the two coils are connected in series with the same polarity, what is the total inductance $L$?