GATE Electrical Engineering (EE) 2018 Solved Paper

Question : 36 of 65

Marks: +1, -0

A transformer with toroidal core of permeability

µ

is shown in the figure. Assuming uniform flux density across the circular core cross-section of radius

r ≪ R

, and neglecting any leakage flux, the best estimate for the mean radius

R

Solution:

v_{P}=N_{P} \;{d\∅}/{d t}=N_{P} \;{d}/{d t}(\;{N_{P} i_{P}}/{R_{l}})

R_{l}=

reluctance

v_{P}=\;{N_{P}^{2}}/{R_{l}} \;{d(I \sin ω t)}/{d t}=\;{N_{P}^{2}}/{R_{l}} × ω I \cos ω t=V \cos ω t

V=\;{N_{P}^{2} ω I}/{R_{l}}=\;{N_{P}^{2} ω I}/{{l}/{µ A}}=\;{µ N_{P}^{2} ω I A}/{l}=\;{µ N_{P}^{2} ω I π r^{2}}/{2 π R}

Hence,

R=\;{µ I r^{2} N_{P}^{2} ω}/{2 V}

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