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3.1 (a) An ideal single-phase two-winding transformer with turns ratio a, = N1/N2 is con- nected with a series impedance Z2 across winding 2. If one wants to replace Z2, with a series impedance Z, across winding 1 and keep the terminal behavior of the two cir- cuits to be identical, find Zj in terms of Zz. (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 impendance by a??

3.1 (a) An ideal single-phase two-winding transformer with turns ratio a, = N1/N2 is con- nected with a series impedance Z2 across winding 2. If one wants to replace Z2, with a series impedance Z, across winding 1 and keep the terminal behavior of the two cir- cuits to be identical, find Zj in terms of Zz. (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 impendance by a??

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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PROBLEMS SECTION 3.1 3.1 (a) An ideal single-phase two-winding transformer with turns ratio a, = N1/N2 is con- nected with a series impedance Z, across winding 2. If one wants to replace Z,, with a series impedance Z, across winding 1 and keep the terminal behavior of the two cir- cuits to be identical, find Z¡ 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 impendance by a?? 3.2 An ideal transformer with N1 = 2000 and N2 = 500 is connected with an impedance Z2, across winding 2, called secondary. If V = 1000 /0° V and I = 5 /-30° A, determine V2, I2, Z2, and the impedance Z', which is the value of Z2 referred to the primary side of the transformer. 3.3 Consider an ideal transformer with N1 = 3000 and N2 = 1000 turns. Let winding 1 be connected to a source whose voltage is e1(t) = 100(1 - |4) volts for –1 sisl and ei(1) = 0 for |t| > 1 second. A 2-farad capacitor is connected across winding 2. Sketch ei(1), e2(1), i1 (1), and i2(t) versus time t. A single-phase 100-kVA, 2400/240-volt, 60-Hz distribution transformer is used as a step-down transformer. The load, which is connected to the 240-volt secondary wind- ing, absorbs 80 kVA at 0.8 power factor lagging and is at 230 volts. Assuming an ideal transformer, calculate the following: (a) primary voltage, (b) load impedance, (c) load impedance referred to the primary, and (d) the real and reactive power sup- plied to the primary winding. 3.4
Transcribed Image Text:PROBLEMS SECTION 3.1 3.1 (a) An ideal single-phase two-winding transformer with turns ratio a, = N1/N2 is con- nected with a series impedance Z, across winding 2. If one wants to replace Z,, with a series impedance Z, across winding 1 and keep the terminal behavior of the two cir- cuits to be identical, find Z¡ 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 impendance by a?? 3.2 An ideal transformer with N1 = 2000 and N2 = 500 is connected with an impedance Z2, across winding 2, called secondary. If V = 1000 /0° V and I = 5 /-30° A, determine V2, I2, Z2, and the impedance Z', which is the value of Z2 referred to the primary side of the transformer. 3.3 Consider an ideal transformer with N1 = 3000 and N2 = 1000 turns. Let winding 1 be connected to a source whose voltage is e1(t) = 100(1 - |4) volts for –1 sisl and ei(1) = 0 for |t| > 1 second. A 2-farad capacitor is connected across winding 2. Sketch ei(1), e2(1), i1 (1), and i2(t) versus time t. A single-phase 100-kVA, 2400/240-volt, 60-Hz distribution transformer is used as a step-down transformer. The load, which is connected to the 240-volt secondary wind- ing, absorbs 80 kVA at 0.8 power factor lagging and is at 230 volts. Assuming an ideal transformer, calculate the following: (a) primary voltage, (b) load impedance, (c) load impedance referred to the primary, and (d) the real and reactive power sup- plied to the primary winding. 3.4
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