Handwrite and step by step solutions Consider the transformer with the secondary terminated in a load resistance R, asshown. This as a real transformer with a coupling coefficient k <1. Assuming ACexcitation at a frequency , derive1₂voltagethe frequency-dependenttransformation ratio V₂ (@)/V(@) interms of the turns ratio, coupling V₁coefficient, and mutual inductanceL=k√ √LL₂ between the primaryand secondary coils. Show that theV₂imperfect coupling gives the circuit a low-pass characteristic with a time constantT=L₂(1-k²)/R₁. Note the orientation of the windings in the figure, as well as thedirection of current I2, which imply the following two-port network equationsV₁ = jwL₂1₁-jwLm¹2V₂ = jwLm11-jwL₂I₂R₂

Given data: The load load resistance is RL. The current in the source side winding is I1 and current…

Consider the transformer with the secondary terminated in a load resistance R, as shown. This as a real transformer with a coupling coefficient k<1. Assuming AC excitation at a frequency @, derive 1₂ the frequency-dependent voltage transformation ratio V₂ (@)/(a) in terms of the turns ratio, coupling V coefficient, and mutual inductance L=k√ √LL₂ between the primary and secondary coils. Show that the imperfect coupling gives the circuit a low-pass characteristic with a time constant t = L₂(1-k²)/ R₂. Note the orientation of the windings in the figure, as well as the direction of current 72, which imply the following two-port network equations V₁ = jwL₂1₁-jwLm¹₂ V₂ = jwLm-jwL₂1₂ R₂

Consider the transformer with the secondary terminated in a load resistance R, as shown. This as a real transformer with a coupling coefficient k<1. Assuming AC excitation at a frequency @, derive 1₂ the frequency-dependent voltage transformation ratio V₂ (@)/(a) in terms of the turns ratio, coupling V coefficient, and mutual inductance L=k√ √LL₂ between the primary and secondary coils. Show that the imperfect coupling gives the circuit a low-pass characteristic with a time constant t = L₂(1-k²)/ R₂. Note the orientation of the windings in the figure, as well as the direction of current 72, which imply the following two-port network equations V₁ = jwL₂1₁-jwLm¹₂ V₂ = jwLm-jwL₂1₂ R₂

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter3: Power Transformers

Section: Chapter Questions

Problem 3.7P: Consider a source of voltage v(t)=102sin(2t)V, with an internal resistance of 1800. A transformer...

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Consider an ideal transformer with N1=3000andN2=1000 turns. Let winding 1 be connected to a source whose voltage is e1(t)=100(1| t |)volts for 1t1ande1(t)=0 for | t |1 second. A2- farad capacitor is connected across winding 2. Sketch e1(t),e2(t),i1(t),andi2(t) versus time t.
A single-phase, 50-kVA,2400/240-V,60-Hz distribution transformer has the following parameters: Resistance of the 2400-V winding: R1=0.75 Resistance of the 240-V winding: R2=0.0075 Leakage reactance of the 2400-V winding: X1=1.0 Leakage reactance of the 240-V winding: X2=0.01 Exciting admittance on the 240-V side =0.003j0.02S (a) Draw the equivalent circuit referred to the high-voltage side of the transformer. (b) Draw the equivalent circuit referred to the low-voltage side of the transformer. Show the numerical values of impedances on the equivalent circuits.
The ideal transformer windings are eliminated from the per-unit equivalent circuit of a transformer. (a) True (b) False
For an ideal 2-winding transformer, the ampere-turns of the primary winding, N1I1 is equal to the ampere-turns of the secondary winding, N2I2 (a) True (b) False
For a short-circuit test on a 2-winding transformer, with one winding shorted, can you apply the rated voltage on the other winding? (a) Yes (b) No
(a) An ideal single-phase two-winding transformer with turns ratio at=N1/N2 is connected with a series impedance Z2 across winding 2. If one wants to replace Z2, with a series impedance Z1 across winding 1 and keep the terminal behavior of the two circuits to be identical, find Z1 in terms of Z2. (b) Would the above result be true if instead of a series impedance there is a shunt impedance? (c) Can one refer a ladder network on the secondary (2) side to the primary (1) side simply by multiplying every impedance byat2 ?
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The ratings of a three-phase three-winding transformer are Primary(1): Y connected 66kV,15MVA Secondary (2): Y connected, 13.2kV,10MVA Tertiary (3): A connected, 2.3kV,5MVA Neglecting winding resistances and exciting current, the per-unit leakage reactances are X12=0.08 on a 15-MVA,66-kV base X13=0.10 on a 15-MVA,66-kV base X23=0.09 on a 10-MVA,13.2-kV base (a) Determine the per-unit reactances X1,X2,X3 of the equivalent circuit on a 15-MVA,66-kV base at the primary terminals. (b) Purely resistive loads of 7.5 MW at 13.2 kV and 5 MW at 2.3kV are connected to the secondary and tertiary sides of the transformer, respectively. Draw the per- unit impedance diagram, showing the per-unit impedances on a 15-MVA,66-kV base at the primary terminals.
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An ideal transformer with N1=1000andN2=250 is connected with an impedance Z22 across winding 2. If V1=10000VandI1=530 A, determine V2,I2,Z2, and the impedance Z2, which is the value of Z2 referred to the primary side of the transformer.
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