Transformer Equation Confusion

I have read some posts on here which I think to revolve around my problem too but couldn't really understand the explanations.

So basically, I have seen how the Transformer equation is derived: $$\frac{N_S}{N_P} = \frac {V_S}{V_P}$$ and in the derivations, from what I understand they all revolve around the certain fact: changing flux created by primary coil induces an e.m.f in the primary coil itself which is equal to the primary source voltage $$V_P = -N_P\frac{d\phi}{dt}$$ However wouldn't this mean that now in the primary coil there is $$2V_P$$ because the induced emf from that equation is equal to primary source emf? Thank you for your help in advance!

• Hint: think about how Kirchhoff's Voltage Law applies here. – The Photon Apr 22 at 17:39
• Yes kirchhoff's law just says that the p.d a across the primary coil is the same as the p.d of the source; however this p.d is the cause of a change in magnetic field which in turn causes a change in flux thus inducing an e.m.f in the primary coil however why does this induced e.m.f have to be equal to the p.d provided by the source? – Luca Ion Apr 23 at 7:20