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- Ideal transformer equations
By Faraday's law of induction:
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 , and subscripts P and S denote primary and secondary.
Combining the ratio of eq. 1 and eq. 2:
where for a step-up transformer a 1.
By the law of conservation of energy, apparent, real and reactive power are each conserved in the input and output:
where is apparent power and is current.
Combining Eq. 3 and Eq. 4 with this endnote gives the ideal transformer identity:
where is the primary winding self-inductance and is the secondary winding self-inductance.
By Ohm's law and the ideal transformer identity:
where is the load impedance of the secondary circuit and is the apparent load or driving point impedance of the primary circuit, the superscript denoting impedance referred to the primary. (en)
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