What is the primary purpose of a transformer?

Transformer: two coils of wire wound around a common iron core; AC current in the PRIMARY coil creates a changing magnetic field; the changing magnetic field induces an AC voltage in the SECONDARY coil. No direct electrical connection between primary and secondary — energy transfers through magnetic field. Turns ratio: V_secondary / V_primary = N_secondary / N_primary, where N = number of turns. STEP-UP transformer (more turns on secondary): increases voltage, decreases current proportionally. STEP-DOWN transformer (fewer turns on secondary): decreases voltage, increases current proportionally. Power (P = VI) is approximately conserved (minor losses to heat); higher voltage = lower current for the same power. Why transformers matter: ELECTRICAL TRANSMISSION uses very high voltage (250-765 kV) for long distances because higher voltage = lower current = less I²R power loss in wires; transformers step down to lower voltages near use (distribution lines 4-25 kV; household 120/240V US, 230V UK). Transformers ONLY work with AC because they require a CHANGING magnetic field to induce voltage in the secondary — DC creates a constant field that doesn't induce. Common applications: (1) UTILITY POWER GRID — countless transformers from generators (10s of kV) → transmission lines (100s of kV) → distribution (kV) → service drops (240V) → appliances (5-120V); (2) ELECTRONIC POWER SUPPLIES — step down household 120V AC to lower AC for further conversion to DC (older devices); (3) AUDIO — impedance matching, isolation; (4) WELDING — step down to provide high current at low voltage; (5) DOORBELLS — step down to 16-24V for the chime. Losses: COPPER LOSS (I²R in wire), CORE LOSS (eddy currents and hysteresis in iron) — minimized by using laminated cores and good materials. Modern switched-mode power supplies use small high-frequency transformers, more efficient than older 60 Hz transformers.