Objective: To determent the efficiency and regulation of a single phase transformer by conducting (a) open circuit test and (b) short circuit test.
The physical basis of the transformer is mutual induction between two circuits linked by a common magnetic field . Transformer is required to pass eletrical energy from one circuit to another, via the medium of the pulsating magnetic field, as efficiently and economically as possible. This could be achived using either iron or steel which serves as a good permeable path for the mutual magnetic flux.
Let an alternating voltage V1 be applied to primary coil of N1 turns linking a suitable iron core. A current flows in the coil , establishing a
flux in the core. This flux induces an emf e1 in the coil to counterbalance the applied voltage V1. This emf is
Assuming sinusoidal time variation of the flux , let Then,
The r.m.s value of this voltage is given by :
Now if there is a secondary coil of N2 turns, wound on the same core, then by mutual induction an emf e2 is developed therein. The
r.m.s value of this voltage is given by :
where is the maximum value of the (sinusoidal) nflux linking the secondary coil ().
If it is assumed that then the primary and secondary emf bear the following ratio:
Note that in actual practice, since some of the flux paths linking the primary coil do not link the secondary coil and similarly
some of the flux paths linking the secondary coil do not link the primary coil. The fluxes which do not link both the coils are called
"Leakage Fluxes" of the primary and secondary coil.
Although the iron core is highly permeable, it is not possible to generate a magnetic field in it without the application of a small m.m.f
(magnato motive force), denoted by Mm.
where Ph, Pe, Pc are hysteresis, eddy current and core losses respectively, Kh and Ke are constants which depend upon on the
magnetic material, and Bmax is the maximum flux density in the core.
Equivalent Circuit of a Practical Transformer:
Development of Transformer Equivalent Circuit:
The practical transforme has coils of finite resistance. Though this resistance is actually distributed uniformly, it can be conceived as
concentrated. Also, all the flux produced by the primary current cannot confined into a desired path completely as an eletric current.
On account of the leakage flux, both the windings have a voltage drop which is due to 'leakage reactance' . The transformer shown in
the figure 1 can be resolved into an equivalent circuit as shown in figure 2(a) in which the resistance and leakage reactance of primary
and secondary respectively are represented by lumped R1, X1, R2, X2 . This equivalent circuit can be simplified by referring all quantities
in the secondary side of the transformer to primary side and is shown in figure 2(b).
Approximate Equivalent Circuit of Transformer: