Transformers

A transformer changes an ac voltage to a larger or smaller one using mutual induction. Two insulated coils, the primary with Np turns and the secondary with Ns turns, are wound on a soft-iron core, one over the other or on separate limbs.

AC in the primary sets up an alternating flux in the core. The same flux φ per turn threads the secondary, giving es = −Ns dφ/dt, and it induces a back emf ep = −Np dφ/dt in the primary.

For an ideal transformer (primary resistance negligible, no flux leakage, small secondary current) vp = ep and vs = es, so vs/vp = Ns/Np.

If no energy is lost, input and output power are equal, ip vp = is vs, so is/ip = Np/Ns = vp/vs. These ratios hold for peak and rms values alike.

Ns > Np gives a step-up transformer: higher voltage, lower current. Ns < Np gives a step-down transformer: lower voltage, higher current.

Example from the text: with 100 primary and 200 secondary turns, 220 V at 10 A in becomes 440 V at 5.0 A out.

Real transformers lose some energy. Flux leakage is reduced by winding one coil over the other; winding resistance by thick wire; eddy currents in the core by laminating it; hysteresis by a core material with a small hysteresis loss. A well-designed transformer can be more than 95% efficient.

Power is sent over long distances at high voltage so that the current, and with it the I²R loss in the lines, is small. Sub-stations and pole transformers then step the voltage down in stages for homes.