What is Ideal Transformer ?
An ideal transformer is a transformer with the following assumptions:
- Permeability of transformer is infinite.
- Iron loss in the transformer core are zero.
- Resistance of transformer winding is zero.
- No magnetic leakage flux, so coefficient of coupling is 1.
- Magnetization curve of transformer is linear.
Operation of Ideal transformer under load
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| Schematic diagram of an ideal, 1-phase transformer under load |
When a finite impedance load ZL is connected across the secondary terminals of a 1-phase transformer as shown in above figure, the load current I2 flows through the secondary winding and the load.load current I2 is given by:-
I2 = V2 / ZL
How will MMFs Produce ?
A voltage source V1 is connected to the primary winding. Due to this voltage V1 primary current I1 flowing through N1 number of turns in the primary winding produces an MMF N1.I1 which creates the flux Ⲫ in the core. This flux links with the secondary coil and induces an EMF of E2 in the secondary winding. This source of EMF circulates a current I2 through the secondary winding and the load. This current I2 flowing through the secondary winding with N2 number of turns produces an MMF N2.I2 .
The primary MMF N1.I1 is thus the cause and the secondary MMF N2.I2 is the effect.
According to Lenz's law, the secondary MMF will try to oppose the primary MMF. In ideal condition, when there is no flux leakage, the two MMFs exactly balance each other, i.e., they are exactly equal in magnitude and opposite in phase.
i.e. N1 I1 = - N2 I2
or, I1 / I2 = - N2 / N1
or, I1 = - I2 / a
primary and secondary currents are thus in exact phase opposition.
If the Load current varies:-
When the load current I2 increases due to any changes in load impedance, the secondary MMF N2 I2 also increases. This MMF produces and opposes flux in core that tries to reduce the main mutual flux Ⲫ. As soon as the flux Ⲫ reduces, the self EMF E1 in the primary winding also reduces. Thus, the opposition to the primary supply voltage V1 reduces (remember, at steady operating conditions, V1 is exactly balanced by E1 in an ideal transformer). The supply voltage V1 can now send more current to the primary winding causing I1 to increase and thus the primary MMF N1 I1 is also increased. This increased amount of primary MMF restores the main flux Ⲫ once again to its original value.
The mutual flux Ⲫ in a transformer is thus always more or less held at a constant value.
Opposite process happens when the load current is reduced. Any variations in the load current I2 is thus balanced by a proportional variations in the supply current I1 so as to keep the the main flux Ⲫ constant in the core. The main mutual flux is thus always maintained at a value which ensures that the primary EMF E1 is always equal and opposite to V1 (neglecting voltage drops in the winding of an ideal transformer).
Note that the resultant MMF in a transformer that maintains the mutual flux in the core is due to the combined actions of primary and secondary MMFs.
Phasor diagram of ideal transformer under load:-
Assume the load is R-L load
I2 lagging behind the voltage V2 by the phase angle Ө
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| Phasor diagram of ideal transformer operation with load |
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