Answer: A transformer works on mutual induction; the RMS induced EMF in a winding of N turns is \(E=4.44\,f\,\Phi_m N\).
Construction (in brief): two windings, the primary (\(N_1\) turns) and the secondary (\(N_2\) turns), are wound on a laminated silicon-steel core. The windings are electrically separate and linked only magnetically through the core. (Diagram to draw: a rectangular core, primary on the left limb connected to the AC supply \(V_1\), secondary on the right limb connected to the load, mutual flux \(\Phi\) shown circulating in the core.)
Working principle: when an alternating voltage \(V_1\) is applied to the primary, an alternating current flows and sets up an alternating flux \(\Phi\) in the core. This flux links both windings. By Faraday's law, the changing flux induces an EMF \(E_1\) in the primary (self-induction) and \(E_2\) in the secondary (mutual induction). If a load is connected, current flows in the secondary and power is transferred from primary to secondary at the same frequency, with no electrical connection. A transformer cannot work on DC because a steady flux induces no EMF.
EMF equation: let the flux be \(\Phi=\Phi_m\sin\omega t\). The EMF per turn is
\[e=-\frac{d\Phi}{dt}=-\omega\Phi_m\cos\omega t=\omega\Phi_m\sin(\omega t-90^\circ).\]
Maximum EMF per turn \(=\omega\Phi_m=2\pi f\Phi_m\). RMS value per turn \(=\dfrac{2\pi f\Phi_m}{\sqrt2}=4.44\,f\Phi_m\).
For \(N_1\) and \(N_2\) turns:
\[E_1=4.44\,f\,\Phi_mN_1,\qquad E_2=4.44\,f\,\Phi_mN_2.\]
(Using \(\Phi_m=B_mA\): \(E=4.44\,f\,B_mAN\).) The induced EMF lags the flux by 90°.
Transformation ratio: \(K=\dfrac{E_2}{E_1}=\dfrac{N_2}{N_1}\approx\dfrac{V_2}{V_1}=\dfrac{I_1}{I_2}\). \(K>1\): step-up; \(K<1\): step-down.
