• Tags: transformer, turns-ratio, efficiency
• Difficulty: Moderate

A transformer works on mutual induction: an AC current in the primary coil creates a changing magnetic flux that induces an EMF in the secondary coil. For an ideal transformer: V_s/V_p = N_s/N_p (turns ratio k), and V_pI_p = V_sI_s (power conservation), so I_s/I_p = N_p/N_s = 1/k. Step-up (k > 1) increases voltage but decreases current. Step-down (k < 1) does the opposite. Impedance transformation: Z_s = k^2 * Z_p (used in impedance matching). Real transformers have losses: (1) Copper losses: I^2R heating in windings — minimized by using thick, low-resistance wire. (2) Eddy current losses: circulating currents in the core — minimized by using laminated core. (3) Hysteresis losses: energy spent magnetizing/demagnetizing core — minimized by using soft iron (narrow hysteresis loop). (4) Flux leakage: not all flux links both coils. Efficiency = (V_sI_s)/(V_pI_p) x 100%. Transformers only work with AC because DC produces constant flux (no induced EMF).