**1. Equivalent circuit of Transformer**

The term equivalent circuit of a machine means the combination of fixed and variable resistances and reactances, which exactly simulates performance and working of the machine.

For a transformer, no load primary current has two components,

I

_{m }= I_{o }sinΦ_{o}= Magnetizing component I

_{c }= I_{o }cosΦ_{o}= Active component I

_{m }produces the flux and is assumed to flow through reactance X_{o }called no load reractance while I_{c }is active component representing core losses hence is assumed to flow through the reactance R_{o}. Hence equivalent circuit on no load can be shown as in the Fig. 1. This circuit consisting of R_{o }and X_{o }in parallel is called exciting circuit. From the equivalent circuit we can write,R

_{o}= V_{1}/I_{c}and X

_{o}= V_{1}/I_{m}Fig. 1 No load equivalent circuit |

When the is connected to the transformer then secondary current I

_{2 }flows. This causes voltage drop across R_{2 }and R_{2}. Due to I_{2}, primary draws an additional current I

_{2}**'**= I_{2}/ K. Now I_{1}is the phasor addition of I_{o}and I_{2}**'**. This I_{1}causes the voltage drop across primary resistance R_{1}and reactance X_{1}. But in the equivalent circuit, windings are not shown and it is further simplified by transferring all the values to the primary or secondary. This makes the transformer calculation much easy.

So transferring secondary parameters to primary we get,

R

R

_{2}**'**= R_{2}/K^{2 }, X_{2}**'**= X_{2}/K^{2}**'**, Z_{2}**'**= Z_{2}/K^{2 }While E

_{2}**'**= E_{2}/K**'**I_{2}**'**= K I_{2}Where K = N

_{2 }/N_{1 }_{ } While transferring the values remember the rule that

Low voltage winding High current Low impedance

High voltage winding Low current High impedance

Thus the exact equivalent circuit referred to primary can be shown as in the Fig. 3.

E

Fig. 3 Exact equivalent circuit referred to primary |

Similarly all the primary value can be referred to secondary and we can obtain the equivalent circuit referred to secondary.

R_{1}**'**= K^{2 }R_{1 }, X_{1}**'**= K^{2 }X_{1}, Z_{1}**'**= K^{2 }Z_{1}E

_{1}**'**= K E_{1}, I_{o}**'**= I_{1 }/K**'**I_{o}**'**= I_{o }/K Similarly the exciting circuit parameters also gets transferred to secondary as R

_{o}**'**and X_{o }**'**. The circuit is shown in the Fig.4.Fig. 4 Exact equivalent circuit referred to secondary |

Now as long as no load branch i.e. exciting branch is in between Z

_{1 }and Z_{2}**'**, the impedances can not be combined. So further simplification of the circuit can be done. Such circuit is called approximate equivalent circuit.__1.1 Approximate Equivalent Circuit__

To get approximate equivalent circuit, shift the no load branch containing R

So approximate equivalent circuit referred to primary can be as shown in the Fig. 5._{o }and X_{o }_{ }to the left of R_{1 }and X_{1}. By doing this we are creating an error that the drop across R_{1 }and X_{1}due to I_{o}is neglected. Hence such an equivalent circuit is called approximate equivalent circuit.Fig. 5 Approximate equivalent circuit referred to primary |

In this circuit now R

_{1 }and R_{2}**'**can be combined to get equivalent resistance referred to primary R_{1e }as discussed earlier. Similarly X_{1}and X_{1}**'**can be combined to get X_{1e}. And equivalent circuit can be simplified as shown in the Fig. 6.Fig. 6 |

_{1e }= R

_{1 }+ R

_{2}

**'**= R

_{1 }+ R

_{2}/K

^{2 }

X

_{1e }= X

_{1 }+ X

_{2}

**'**= X

_{1 }+ X

_{2}/K

^{2 }

Z

_{1e}= R

_{1e }+ j X

_{1e }

R

_{o }= V

_{1 }/I

_{c }and X

_{o }=

_{ }V

_{1 }/I

_{m }

I

_{c }= I

_{o }cosΦ

_{o}and Im = I

_{o }sinΦ

_{o}

In the similar fashion, the approximate equivalent circuit referred to secondary also can be obtained.

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Okay I have one doubt,why we represent "Ro" in the equivalent circuit & also have one doubt why we connected "Ro & Xo " across the supply.Why don't we connected in series.

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