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Magnetic leakage of Single Phase Transformer

The magnetic Leakage flux:

When the a.c power supply is applied to the primary winding of a transformer, the primary winding produces magnetic flux φ which flows through the Iron core of the transformer and the magnetic flux cuts the secondary winding of the transformer. But, all flux of primary winding does not cut the secondary winding, some part of flux i.e φL1 completes its magnetic circuit by passing through the air rather than around the core which is shown in fig. This leakage flux is produced due to the primary-amp turn ( m.m.f ) existing between point a and b. This leakage flux φL1 completes the magnetic circuit in the portion ( a-b ) .Hence, this flux is known as primary leakage flux and is proportional to the primary ampere-turns. This flux φL1 is in time phase with primary current I1 and induces an e.m.f eL1 in primary winding only.

Similarly, due to secondary ampere-turns ( m.m.f) across points c and d , leakage flux is produced φL2 which is linked with secondary winding only,( not linked with primary winding ). This φL2is in time phase with I2 and produces a self-induced e.m.f eL2 in the secondary winding. The both leakage flux at primary and secondary fully depends on the load of the transformer. If load of transformer increase, leakage flux will simultaneously increase.

The leakage flux linking with each winding , produce a self induced e.m.f in the winding . and this e.m.f is equivalent to a small choker or inductive coil in series with each winding. And the voltage drop in each series coil is equal to that produced by leakage flux. A transformer with to an ideal transformer is equivalent to an ideal transformer with the inductive coil connected in both primary and secondary circuit as shown in the figure.

Let,X1 is primary leakage reactance and X2 is secondary leakage reactance of a transformer.
Therefore, X1 = eL1 / I1 ( where I1 is Primary current and eL1 is self-induce e.m.f in primary winding )
X2= eL2 / I2 ( where I2 is Secondary current and eL2 is self induce e.m.f in Secondary winding )
Due to leakage reactance, the reactive drop should be added with the resistive drop at both windings.Therefore, The reactive drop in primary winding = I1X1 and the rective drop in secondary winding = I2X2.

Please note that the leakage fluxes of the transformer can be minimized by sectionalizing and interleaving the primary and secondary windings which is shown in the figure below.

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