Transformer Calculator

In an ideal transformer, the turns ratio (N₁/N₂) equals the voltage ratio (V₁/V₂) and is inversely proportional to the current ratio (I₂/I₁). This means that if you have a 10:1 turns ratio, the primary voltage will be 10 times the secondary voltage, but the secondary current will be 10 times the primary current. This relationship follows from the principle of conservation of energy and is fundamental to transformer operation. For example, a transformer with 1000 primary turns and 100 secondary turns (10:1 ratio) connected to 240V will output approximately 24V.

Real transformers have several losses that make them less than 100% efficient: copper losses (I²R heating in the windings), core losses (hysteresis and eddy currents in the iron core), and flux leakage (not all magnetic flux links both windings). These factors mean real transformers typically achieve 95-99% efficiency in large power applications, and less in smaller units. Core losses are constant regardless of load, while copper losses increase with load. Temperature also affects performance - most transformers are designed for specific temperature ranges and may need cooling systems.

Transformers are crucial in power distribution because they allow efficient power transmission over long distances. Power is transmitted at high voltage (hundreds of kV) to minimize current and therefore reduce I²R losses in the transmission lines. For example, transmitting 100 MW of power at 500 kV instead of 10 kV reduces current by a factor of 50, reducing power loss by a factor of 2,500. Step-up transformers at power plants increase voltage for transmission, while step-down transformers near end users reduce voltage to safe, usable levels (e.g., 240V or 120V for homes).