A transformer has two coils wound on a common core having self-inductances, L₁ = 1H, L2 = 2 H, and a mutual inductance, M = 0.5 H.

The currents are i₁ = cos (120 лt) A and i₂ = 0.5 cos (120 лt) A. Assuming a positive mutual inductance for the set of coils, use Faraday's Law of induction to determine v₁ and v₂. Show all of the details.