# Transformer Voltage vs. Frequency

 P: 1,017 For the transformer equation, youre right, the turns ratio equation does hold. The 4.44f... equation is an approximation. If you assume the voltage across the primary is purely sinusoidal and no harmonics are present, $$V_p=V_{max}sin\omega t$$ This causes a current $$I_p=I_{max}sin(\omega t+\theta)$$ where the phase difference exists beacause of the inductance of the primary coil. This current creates a magnetic flux $$\phi _p=\phi _{max} sin(\omega t+ \theta)$$ which is in phase with the current. Now, the voltage induced in the secondary is given by Lenz's Law: $$E_s=-n\frac{d\phi}{dt}$$ where n is the number of turns of the secondary This gives $$E_s=n\phi _{max}\omega sin(\omega t+\theta)$$ $$\omega =2\pi f$$ This secondary induced voltage is approximated by $$E_s=4.44nf\phi$$ As for the hysteresis problem, I'm sure you could find the equation of the hysteresis curve online. From there you know the limiting value of magnetic flux. Using that and the above discussion you could find the relation between frequency and voltage. Hope that helps. Chaos