Q.A transformer increases an alternating e.m.f. from 220V to 880V. If primary coil has 1000 turns, the number of turns in the secondary coil are ______.

A transformer uses mutual inductance to change an alternating voltage from one value to another. Two electrically-insulated coils, the primary and the secondary, are wound on a common soft-iron core that channels nearly all of the primary's flux through the secondary as well ($K\approx1$). A changing primary current produces a correspondingly changing flux $\Phi$ common to both coils, inducing emfs $e_p=-N_p\frac{d\Phi}{dt}$ and $e_s=-N_s\frac{d\Phi}{dt}$ in the primary and secondary respectively, giving the transformer equation $\frac{e_s}{e_p}=\frac{N_s}{N_p}$. …