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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: (a) 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)

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: (a) 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)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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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 was limited to around 5A/mm? for this load. (c) Parameter Value Units Definition RC 1400 Core Loss Resistance Magnetising Reactance Equivalent Winding Resistance Equivalent Leakage Inductance Number of turns in primary winding Number of turns in secondary winding XM 400 Ω Rleq | Xleq | Np 2.4 Ω Ω 100 10 Ns Ас 10,000 mm? Iron Core cross section Primary winding wire diameter Secondary winding wire diameter 3 Dwp Dwr mm mm Table Q3
Transcribed Image Text:(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 was limited to around 5A/mm? for this load. (c) Parameter Value Units Definition RC 1400 Core Loss Resistance Magnetising Reactance Equivalent Winding Resistance Equivalent Leakage Inductance Number of turns in primary winding Number of turns in secondary winding XM 400 Ω Rleq | Xleq | Np 2.4 Ω Ω 100 10 Ns Ас 10,000 mm? Iron Core cross section Primary winding wire diameter Secondary winding wire diameter 3 Dwp Dwr mm mm Table Q3
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