Elementary Theory of an Ideal Transformer

ELEMENTARY THEORY OF AN IDEAL TRANSFORMER

An ideal transformer is one which has no losses i.e., its windings have no ohmic resistance, there is no magnetic leakage and hence it does not have I²R and core losses. In other words, an ideal transformer consists of two purely inductive coils wound on a loss-free core. But it is impossible to realize such a transformer in practice.

Consider an ideal transformer in Figure 1.9 whose secondary is open and whose primary is connected to sinusoidal alternating voltage V₁. This potential difference causes an alternating current to flow in the primary. Primary coil is purely inductive and secondary is open (no output), so primary draws the magnetizing current I_µ only. Function of I_µ is to magnetize the core (i.e.,) the core is act like a magnetic material. It is small in magnitude and lags V₁ by 90°. The magnetizing current I_µ produces an alternating flux in the core which is proportional to current (assuming permeability of the magnetic circuit to be constant). I_µ is in phase with flux φ. The changing flux is linked with the primary and secondary winding. Due to the alternating flux, a self induced emf is produced in the primary which is equal and opposite to V₁ and donated as E₁. It is called as counter emf or back emf on the primary winding.

Similarly, an induced emf E₂ is produced in the secondary winding, because alternating flux is also linking with secondary winding. This emf is called as mutually induced emf. E₂ is in opposition to V₁ and its magnitude is proportional to the rate of change of flux and number of secondary turns.