Iron core with pr The transformer shown consists of a long wire coincident with the z-axis and carrying a current I = Io coswt, coupling magnetic energy to a toroidal coil situated in the x-y plane and centered at the origin. The toroidal coil uses iron material with permeability μ. The tightly wound coil of N turns serves to induce voltage Vem f as shown in the figure. a. Develop an expression for Vem f b. Calculate Vemf for N = 100, f = 60 Hz, μ = 4000μo, a = 5 cm, b = 6 cm, c= 2 cm, and Io = 50 A

Iron core with pr The transformer shown consists of a long wire coincident with the z-axis and carrying a current I = Io coswt, coupling magnetic energy to a toroidal coil situated in the x-y plane and centered at the origin. The toroidal coil uses iron material with permeability μ. The tightly wound coil of N turns serves to induce voltage Vem f as shown in the figure. a. Develop an expression for Vem f b. Calculate Vemf for N = 100, f = 60 Hz, μ = 4000μo, a = 5 cm, b = 6 cm, c= 2 cm, and Io = 50 A

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Solenoids

A solenoid is a common term for a telephone coil used as an electromagnet. It also refers to any device that uses a solenoid to convert electrical energy into mechanical energy. The device generates a magnetic field from an electric field and uses the magnetic field to produce precise motion. Solenoid valves are often used to change power, such as in-car transmitters or valves, such as in the fuel system.

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V
emf
Iron core with
The transformershown consists of a long wire coincident with the z-axis and carrying a current I = Io coswt, coupling magnetic energy to a toroidal coil situated in the x-y
plane and centered at the origin. The toroidal coil uses iron material with permeability µ. The tightly wound coil of N turns serves to induce voltage Vemf as shown in the figure.
a. Develop an expression for Vem f
b. Calculate Vem f for N = 100, f = 60 Hz, μ = 4000μo, a = 5 cm, b=6 cm, c = 2 cm, and Io = 50 A

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(a) Using Faraday's Law as a starting point prove that the maximum operating voltage of a transformer to avoid magnetic saturation is given by the following equation: Q3 Vrms=4.44N.f.Bmax.Ac where: Vrms = maximum rms operating voltage avoiding magnetic saturation N = number of turns in the winding f= electrical frequency (Hz) Bmax = maximum flux density (T) (typically 1.3T for iron) Ac = Iron core cross sectional area (m²) A single phase transformer has the parameters shown on Table Q3 and is connected to a 230 V and 50 Hz AC supply. Sketch the equivalent circuit and using this determine: (b) (i) The Secondary voltage under Open Circuit (Vsoc) (ii) The Secondary voltage, current and power (W) given a 0.6 Q resistive Load. (iii) The efficiency and voltage regulation at this load Through suitable calculations determine whether the size, weight or cost of this transformer could be reduced such that it operated below a maximum flux density of 1.3 T and the current density in both windings…
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