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I've been a bit confused with how the equation Vp/Vs = Np/Ns came about. From reading a physics textbook, I understand that the voltages came from the emfs ε (primary) and ε (secondary). The primary voltage through the primary coils causes a change in magnetic flux which induces an emf in the secondary coils. From this, I can see why ε (secondary) is equal to Vs, but what I don't understand is why the ε (primary) can be replaced with Vp when the formula for ε (primary) is equal to -N (primary) * delta (flux)/delta (time). I thought this equation is for the induced emf, not the applied voltage from the primary source. Or is the primary voltage equal to an induced emf in the primary coils from iron core ie. if a voltage is applied to a solenoid with N(primary) coils, then would there result in a delta (flux)/delta (time)?

If apply voltage to solenoid, then would applied V= N* (delta flux)/ (delta time)?

which would essentially be the same backwards : induced emf = N* (delta flux)/ (delta time)? Is this true or am I totally wrong?

(ideal wires assumed)

Thank you.