Important Formula Transformer - 1

  

EMF Equation of transformer E = 4.44fNBmax A Where f = Supply frequency in Hz N = Number of winding turns Bmax = Maximum flux density in weber per meter square A = Cross section area of core in meter square Primary induced emf E1 = 4.44fN1Bmax A Secondary induced emf E1 = 4.44fN2Bmax A

 

Voltage transformation ratio ( k ) K = E2 / E1 = V2 / V1 = N2 / N1 = I1 / I2

 

Turns ratio N1 / N2 = E1 / E2 = V1 / V2 = I2 / I1 = 1 / k

 

Volts per turns E2 / N2 = E1 / N1 = 4.44fΦmax The volts per turn ratio remains same for primary winding and secondary winding.

 

No load input power W0 = V1I0 Cos Φ0 Where W0 = No load input power V1 = Supply voltage I0 = No load current Cos Φ0 = No load input power factor

 

Active / working iron loss component Iw = I0 Cos Φ0 Magnetizing current Iµ =  I0 Sin Φ0 No load current I0 = √ ( Iw2 + Iµ2 ) No load power factor angle tan Φ0 =  Iµ / Iw Φ0 = tan – 1 ( Iµ / Iw )

 

Primary current ( vector addition ) I1 = I0 + I2’ Where I0 = No load current I2’ = Reflected secondary current

 

Relation between load flux ( Φ2 ) and reflected load component flux  ( Φ2’ ) ( Φ2 ) = ( Φ2’ ) N2I2 = N1I2’ I2’ = ( N2 / N1 ) I2 I2’ = kI2 OR k = I2’ / I2 = I1 / I2 = N2 / N1 = V2 / V1 Where I2’ = Reflected load current I2 = Load current

 

Transformer secondary resistance, reactance and impedance as referred to primary side R2’ = R2 / k2 X2’ = X2 / k2 Z2’ = Z2 / k2 Where R2, X2 and Z2 are secondary resistance, reactance and impedance respectively and k is voltage transformation ratio Equivalent resistance as refereed to primary side R01 = R1 + R2’       = R1 + R2 / k2

 

Transformer primary resistance, reactance and impedance as referred to secondary side R1’ = k2R1 X1’ = k2X1 Z1’ = k2Z1 Where R1, X1 and Z1 are primary resistance, reactance and impedance Equivalent resistance as refereed to secondary side R02 = R2 + R1’        = R2 + k2R1

 

Shifting of secondary voltage / current from secondary side to primary side , only transformation ratio k is used Secondary voltage as refer to primary side V2’ = V2 / k Similarly, secondary current as referred to primary side I2’ = kI2

 

Leakage reactance XL = eL / I

 

No load resistance R0 and reactance X0 R0 = E1 / Iµ X0 = E1 / Iw Where E1 = Primary induced emf

 

Magnetizing ampere turns = N1I1 Demagnetizing ampere turns = N2I2

 

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