Regarding formula for "transformer" in lecture 7

On page 15 of Lecture 7 slides (Lecture_07.pdf), voltage V1 in the transformer's primary circuit is calculated as V1=N1 * d Phi/ d t. This is straight application of Faraday's law of induction (the first equation on page 8 of the same file). We don't use B or even the cross-section of the magnetic core, simply because here Phi is the same in both primary and secondary circuits. Therefore we use Phi directly. Notice in the figure on page 15, Phi is magnetic flux contained by the magnetic core's cross-section. A coil with N turns has N times this much cross-section. Therefore, we have V1=N1 * d Phi/ d t and V2=N2 * d Phi/ d t.