GATE Electrical Engineering (EE) 2019 Solved Paper

Question : 47 of 65

Marks: +1, -0

The magnetic circuit shown below has uniform cross-sectional area and air gap of

0.2 {cm}

. The mean path length of the core is

40 {cm}

. Assume that leakage and fringing fluxes are negligible. When the core relative permeability is assumed to be infinite, the magnetic flux density computed in the air gap is 1 tesla. With same Ampere-turns, if the core relative permeability is assumed to be 1000 (linear), the flux density in tesla (round off to three decimal places) calculated in the air gap is __________.

Your Answer:

Validate

Solution:

length of the core

(l_{l})=39.8 {cm}

length of the air gap

(l_{d})=0.2 {cm}

We know

{MMF}= {R}_{ {M}} ϕ

{NI}= {R}_{ {M}} ϕ

φ=\;{ {NI}}/{ {R}_{ {M}}}

where

R_{ {M}}=

reluctance

{B}=\;{φ}/{ {A}}

{B}=\;{ {NI}}/{ {R}_{ {M}} {A}}

{B} α \;{1}/{ {R}_{ {M}}}

Case-1 Permeability of the core

(µ_{ {c}})=∞

( {R}_{ {M}})_{1}= {R}_{1}+ {R}_{2}

=\;{ℓ_{c}}/{µ {A}}+\;{ℓ_{ {a}}}/{µ_{0} {A}}

( {R}_{ {M}})_{1}=0+\;{0.2}/{µ_{0} {A}}

Case-2
Permeability of the core

(µ_{ {c}})=1000 µ_{0}

( {R}_{ {M}})_{2}= {R}_{1}+ {R}_{2}

=\;{39.8}/{10^{3} µ_{0} {A}}+\;{0.2}/{µ_{0} {A}}

( {R}_{ {M}})_{2}=\;{1}/{µ_{0} {A}}[0.2398]

\;{ {B}_{1}}/{ {B}_{2}}=\;{( {R}_{ {M}})_{2}}/{( {R}_{ {M}})_{1}}

{B}_{2}=\;{( {R}_{ {M}})_{1}}/{( {R}_{ {M}})_{2}}=\;{0.2}/{0.2398}

{B}_{2}=0.83

Go to Question:

Prev Question

Next Question