Voltage ratio of an ideal transformer

Faraday’s induction law makes induced voltage proportional to turn count and the rate of change of shared magnetic flux. If both windings link the same flux, dividing their voltages gives the turns ratio. Leakage flux and winding resistance change real loaded values. The turns ratio applies to ideal sinusoidal steady-state AC; real voltage drops and losses alter loaded output. Application: Estimate ideal AC voltage transformation from winding turns. The numerical example An ideal transformer with N1=500 and N2=100 gives U2=230·100/500=46 V from a 230 V primary anchors the idea in a concrete measurement case.

For an ideal transformer, transferred apparent power is approximately conserved: U1I1≈U2I2. Current therefore varies inversely with voltage ratio. A step-up transformer gives higher voltage and lower current. Real losses and power factor matter in a practical design. The turns ratio applies to ideal sinusoidal steady-state AC; real voltage drops and losses alter loaded output. The corresponding units are U in V; N dimensionless (turn count). An ideal transformer with N1=500 and N2=100 gives U2=230·100/500=46 V from a 230 V primary. This checks that the reference quantities are compatible.

Steady DC creates no changing flux and therefore no continuous secondary voltage. Primary current can also rise strongly through winding resistance once inductive opposition disappears after the switching transient. Transformers need changing or switched voltage within their designed frequency range. The turns ratio applies to ideal sinusoidal steady-state AC; real voltage drops and losses alter loaded output. Scope: The relationship follows from the same changing magnetic flux linking each turn of both windings. It assumes sinusoidal steady-state AC and ideal coupling. Real transformers have winding resistance, leakage inductance, core losses and voltage drop. DC does not induce continuous secondary voltage after the switching transient. A practical application is Estimate ideal AC voltage transformation from winding turns.

Write the quantity and unit from the variable list next to every value: U in V; N dimensionless (turn count). Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example An ideal transformer with N1=500 and N2=100 gives U2=230·100/500=46 V from a 230 V primary. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. The turns ratio applies to ideal sinusoidal steady-state AC; real voltage drops and losses alter loaded output.

The background states this starting condition: The relationship follows from the same changing magnetic flux linking each turn of both windings. It assumes sinusoidal. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. The turns ratio applies to ideal sinusoidal steady-state AC; real voltage drops and losses alter loaded output.