× Home MCQ Videos Basic Electrical Circuit Theories Electrical Laws Materials Batteries Illumination Generation Transmission Distribution Switchgear Protection Measurement Control System Utilities Safety Transformer Motor Generator Electrical Drives Electronics Devices Power Electronics Digital Electronics

EMF Equation of Transformer | Turns Voltage Transformation Ratio of Transformer

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.

As the current source to primary is sinusoidal, the flux induced by it will be also sinusoidal. Hence, the function of flux may be considered as a sine function. Mathematically, derivative of that function will give a function for rate of change of flux linkage with respect to time. This later function will be a cosine function since d(sinθ)/dt = cosθ. So, if we derive the expression for rms value of this cosine wave and multiply it with number of turns of the winding, we will easily get the expression for rms value of induced emf of that winding. In this way, we can easily derive the emf equation of transformer. secondary induced voltage ideal 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,  As the maximum value of cos2πft is 1, the maximum value of induced emf e is,  To obtain the rms value of induced counter emf, divide this maximum value of e by √2.

This is 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 .



DDASHRATH SURYAWANSHI commented on 11/05/2018
Can we derive this xmer equation by taking magnetic Flux as a function of cos wave.....replay asap.
PPRATHYUSHA commented on 26/04/2018
There is no equivalent circuit
SSURAJ PRAJAPATI commented on 14/03/2018
This is so amazing page
BBIJAY KUMAR commented on 22/02/2018
Better than book
Comments

Related Articles TransformerInsulating OilTransformer RatingEMF Equation of TransformerOil DeteriorationIdeal TransformerOil SamplingTheory of TransformerAcidity TestLeakage ReactanceDissolved Gas AnalysisWater Content TestEquivalent Circuit of TransformerLosses of TransformerVoltage Regulation of TransformerSingle Three Phase Transformer vs Bank of Three Single Phase TransformersParallel operation of TransformersMagnetizing Inrush Current in Power TransformerShell Type TransformerMore Related Articles Transformer TestTransformer TypeTransformer AccessoriesTransformer ProtectionInstrument TransformerNew Articles Fiber Optic Cable SelectionNatural Gas Power GeneratorsHow to Choose the Best Theater Lighting Equipment?How to Make an Electric Water Pump?Voltage Regulators Articles Categories MCQ Contact Us Basic Electrical Circuit Theories Electrical Laws Materials Batteries Illumination Generation Transmission Distribution Switchgear Protection Measurement Control System Utilities Safety Transformer Motor Generator Electrical Drives Electronics Devices Power Electronics Digital Electronics Videos