- 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
EMF Equation of transformer can be established in a very easy way. Actually in electrical power transformer, one alternating electrical source is applied to the primary winding and due to this, magnetizing current flowing through the primary winding which produces alternating flux in the core of transformer. This flux links with both primary and secondary windings. As this flux is alternating in nature, there must be a rate of change of flux. According to Faraday’s law of electromagnetic induction if any coil or conductor links with any changing flux, there must be an induced emf in it.
Since the current source to the primary winding is sinusoidal, the induced flux will also be sinusoidal. Therefore, the flux can be considered a sine function. Mathematically, taking the derivative of this function gives us the rate of change of flux, which is a cosine function d(sinθ)/dt = cosθ. By deriving the rms value of this cosine wave and multiplying it by the number of turns in the winding, we can easily obtain the RMS value of the induced EMF. This is how we derive the EMF equation of a transformer.
Let’s say, T is number of turns in a winding,
Φm is the maximum flux in the core in Wb.
As per Faraday’s law of electromagnetic induction,
Where φ is the instantaneous alternating flux and represented as,
Since the maximum value of cos2πft is 1, the maximum value of the induced EMF (e) is:
To obtain the rms value of induced counter emf, divide this maximum value of e by √2.
This is the EMF equation of transformer.
If E1 & E2 are primary and secondary emfs and T1 & T2 are primary and secondary turns then, voltage ratio or turns ratio of transformer is,
Transformation Ratio of Transformer
This constant is called transformation ratio of transformer , if T2>T1, K > 1, then the transformer is step up transformer. If T2 < T1, K < 1, then the transformer is step down transformer.
Voltage Ratio of Transformer
This above stated ratio is also known as voltage ratio of transformer if it is expressed as ratio of the primary and secondary voltages of transformer.
Turns Ratio of Transformer
As the voltage in primary and secondary of transformer is directly proportional to the number of turns in the respective winding, the transformation ratio of transformer is sometime expressed in ratio of turns and referred as turns ratio of transformer .
