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Transformer concept | Transformer formula | Transformer principle.


An apparatus for reducing or increasing the voltage of an alternating current

A transformer is a passive electrical device that transfers electrical energy from one electrical circuit to another, or multiple circuits. A varying current in any one coil of the transformer produces a varying magnetic flux in the transformer's core, which induces a varying electromotive force across any other coils wound around the same core. Electrical energy can be transferred between separate coils without a metallic (conductive) connection between the two circuits.

Ideal transformer equations
By Faraday's law of induction:
 . . . (eq. 1)
 . . . (eq. 2)
Where  is the instantaneous voltage is the number of turns in a winding, dΦ/dt is the derivative of the magnetic flux Φ through one turn of the winding over time (t), and subscripts P and S denotes primary and secondary.
Combining the ratio of eq. 1 & eq. 2:
Turns ratio  . . . (eq. 3)

Where for a step-down transformer a > 1, for a step-up transformer a < 1, and for an isolation transformer a = 1.
By law of conservation of energyapparentreal and reactive power are each conserved in the input and output:
 . . . . (eq. 4)
Where  is conserved power and  is current.
Combining eq. 3 & eq. 4 with this end note gives the ideal transformer identity:
 . (eq. 5)
Where  is winding self-inductance.
By Ohm's law and ideal transformer identity:
 . . . (eq. 6)
 . (eq. 7)
Where  is the load impedance of the secondary circuit &  is the apparent load or driving point impedance of the primary circuit, the superscript  denoting referred to the primary.

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