- EMF Equation of Transformer Definition: The EMF equation of a transformer is derived using Faraday’s law, indicating the induced EMF based on flux changes and winding turns.
- Magnetizing Current: An alternating current in the primary winding generates a magnetizing current that produces alternating flux in the transformer’s core.
- Sinusoidal Flux and EMF: The sinusoidal primary current creates a sinusoidal flux, and its rate of change (cosine function) determines the induced EMF.
- Voltage and Turns Ratio: The ratio of primary to secondary voltage (voltage ratio) is directly proportional to the ratio of the number of turns in the primary and secondary windings (turns ratio).
- Transformation Ratio: The transformation ratio (K) indicates whether a transformer is step-up (K > 1) or step-down (K < 1), based on the primary and secondary windings.
Emf Equation of Transformer
The EMF Equation of transformer follows from Faraday’s law. On an electrical power transformer an alternating source on the primary drives magnetizing current, and that current produces alternating flux in the core of transformer. The flux links both windings. Because the flux is alternating, its rate of change is not zero. By Faraday’s law of electromagnetic induction, any coil or conductor linking that changing flux has an induced EMF.
The current source on the primary is sinusoidal, so the flux is sinusoidal too. Treat flux as a sine. Its derivative, the rate of change, is a cosine: d(sinθ)/dt = cosθ. Take the rms value of that cosine and multiply by the turns in the winding to get the RMS induced EMF. That product is the EMF equation of a transformer.
Let T be the number of turns in a winding,
Φm the maximum core flux in Wb.
From Faraday’s law of electromagnetic induction,
φ is the instantaneous alternating flux:
The maximum of cos2πft is 1, so the maximum induced EMF (e) is:
The RMS counter EMF is that maximum divided by √2.
That is the EMF equation of the transformer.
If E1 & E2 are the primary and secondary EMFs and T1 & T2 are the primary and secondary turns, the voltage ratio or turns ratio of transformer is
Transformation Ratio of Transformer
That constant is the transformation ratio of transformer . If T2>T1, K > 1 and the unit is a step-up transformer. If T2 < T1, K < 1 and the unit is a step-down transformer.
Voltage Ratio of Transformer
The same ratio is the voltage ratio of transformer when it is written as primary voltage over secondary voltage.
Turns Ratio of Transformer
Primary and secondary voltages are proportional to the turns on those windings, so the same constant is often written as a turns count and called the turns ratio of transformer .
