Consider a single phase transformer with 100 turns on the primary and 200 turns on the secondary. In this question you should account for the magnetizing inductance but ignore leakage inductance, copper losses, and core losses. Assume that the core flux φ, core magnetic field H, and core flux density B are uniform over the cross-section of the core. The iron core has permeability µ and cross-sectional area A and length `. (a) Write im for the current in the primary and λ1 for the flux linked with the primary. You know that the inductance Lm as seen from the primary is defined as Lm = λ1/im. Assuming that the secondary is open circuit, use Amperes law and other relationships to derive a formula for the
Three-Phase Transformers
Three-segment transformers are a type of transformer used to transform voltages of electrical systems into three ranges. Two type transformers are shell-type transformer and core type transformer. In brief, it could be described because of the exquisite kinds of configurations.
Transformer
Ever since electricity has been created, people have started using it in its entirety. We see many types of Transformers in the neighborhoods. Some are smaller in size and some are very large. They are used according to their requirements. Many of us have seen the electrical transformer but they do not know what work they are engaged in.
Consider a single phase transformer with 100 turns on the primary and 200
turns on the secondary. In this question you should account for the magnetizing
inductance but ignore leakage inductance, copper losses, and core losses. Assume
that the core flux φ, core magnetic field H, and core flux density B are uniform over
the cross-section of the core. The iron core has permeability µ and cross-sectional
area A and length `.
(a) Write im for the current in the primary and λ1 for the flux linked with the
primary. You know that the inductance Lm as seen from the primary is defined as
Lm = λ1/im. Assuming that the secondary is open circuit, use Amperes law and
other relationships to derive a formula for the inductance Lm in terms of µ, A, `.
(b) Assuming that the secondary is open circuit, and phasor voltage V = 100∠30o
Volt is applied to the primary coil, use Faraday’s law to compute the core flux as a
time signal φ(t) and the core flux as a phasor Λ.
(c) Now assume the secondary allows a current i2 and has voltage v2. Apply Faraday’s law and Ampere’s law to derive the equations of the transformer and its
equivalent circuit.
(d) Show that the complex power entering the transformer primary is equal to the
complex power leaving the transformer secondary.
(e) Derive the formula for transferring a complex impedance Z1 from the primary
to its equivalent complex impedance Z2 the secondary. (f) State the two forms
(one in terms of currents, the other in terms of flux; they are equivalent) of the dot
convention
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