What is EMF Equation of Electrical Transformer? | Electronicsinfos

EMF Equation of Electrical Transformer

    What is emf equation of transformer

    The Emf Equation of an electrical transformer is a Mathematical Expression that defines the relationship of Primary Induced voltages to Secondary Induced voltages. when we connect the transformer through the alternating supply to the primary side the alternating current is produced on the primary side. This primary current is called induced current which is also alternating in nature. This alternating current produced a flux that is also alternating in nature. The flux passes through the magnetic core which provides a low reluctance path. This primary flux links with the secondary side of the transformer and according to the Faraday law of electromagnetic induction the emf is produced in the secondary side that is directly proportional to the change of primary link flux. The mathematical equation defines that the change of flux for the time defines the induced emf.

    Transformation Ratio of the Transformer

    In electrical engineering, the transformation ratio of a transformer is the ratio of the number of turns in the primary winding to the number of turns in the secondary winding. This ratio determines how voltage is transformed from the primary side to the secondary side. The transformation ratio (K) is calculated using the formula


    where 1 is the number of turns in the primary winding, and 2 is the number of turns in the secondary winding.

    Step-up Transformer


    N2 > N1,


    The transformer steps up in nature in voltage.

    step up transformer

    Step-Down Transformer




    The Transformer is step-down in nature in voltage.

    step down transformer

    So let's do a mathematical expression which defines the EMF equation of the Electrical transformer

    let us say

    Np= No of tunes on primary

    Ns= No of turns on secondary

    Øm = Maximum value of Flux

    f = Frequency (c/s)

    The flux increases from zero to Øm in 1/4 cycle

    The average rate of change of flux = 4Ømf (WB/sec)

    The average EMF induced in each term is = 4*Øm*f (volts)

    Assuming the flux Ø to vary sinusoidally, then a sinusoidal emf

    will be induced in each turn of both windings.

    For a sine wave, form factor = Rms/Mean= 1.11

    RMS emf induced in each turn

    1.11*4*Øm*f (volts)

    RMS emf induced in primary

    Ep= 4.44*Øm*f*Np (volts)

    RMS emf induced in Secondary

    Es= 4.44*Øm*f*Ns (volts)

    At No load, Ep is almost equal to the primary voltage Vp,
    Es is equal to the secondary voltage Vs

    Es∶Ep = Vs:Vp =Ns:Np

    The P= transformation ratio of the transformer

    Alternative Method Of Finding EMF

    EMF = No of turns* Change of flux per unit time

    EMF = - N dØ/dt

    N= number of turns

    dØ= instantaneous flux

    dt = change of time

    minus = minus represents the Lenz law

    Let The Flux Wave Represent by

    Ø=Ømsin wt

    The emf induced in the primary is

    Eind= -N dØ/dt volts

    = -Np*w*Øm*cos wt volts

    =Np*w*sin(wt-90°) volts

    The max value of induced EMF =


    RMS value of Induced EMF =

    4.44*f*Øm*Np volts ∵ in primary

    4.44*f*Øm*Ns volts ∵ in secondary

    Relationship between Voltage and Current

    The relationship between voltage and current is indirect. if the primary voltage is high the primary current is low and vice versa.

    E1/E2 = I2/I1

    Relationship between Voltage and turns

    The relationship of primary voltage E1 is a direct relation to primary turns N1
    E1/E2 = N1/N2

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