GATE Papers >> EEE >> 2018 >> Question No 36

Question No. 36 EEE | GATE 2018

A transformer with toroidal core of permeability $ \mu $ is shown in the figure. Assuming uniform flux density across the circular core cross-section of radius $ r\ll\;R $ , and neglecting any leakage flux, the best estimate for the mean radius R is


Answer : (D) $ \frac{\mu Ir^2N_P^2\omega}{2V} $

Solution of Question No 36 of GATE 2018 EEE Paper

since secondary is open circuited, then there is no flux due to secondary 

Hence, ratio of current & voltage is impedance of primary

$\begin{array}{l}\frac{\mathrm V}{\mathrm I}=\mathrm{ωL}\\\mathrm L=\frac{\mathrm V}{\mathrm{ωI}}\end{array}$

L (pri) = $\frac{{\mathrm{μN}}_\mathrm p^2\mathrm A}{\mathcal l}=\frac{{\mathrm{μN}}_\mathrm p^2(\mathrm{πr}^2)}{2\mathrm{πR}}=\frac{\mathrm V}{\mathrm{Iω}}$

R = $\frac{{\mathrm{μIN}}_\mathrm p^2\mathrm r^2}{2\mathrm V}$

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