{"id":190989,"date":"2025-02-14T04:46:25","date_gmt":"2025-02-14T04:46:25","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=190989"},"modified":"2025-02-14T04:46:27","modified_gmt":"2025-02-14T04:46:27","slug":"a-rectangular-magnetic-core","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/14\/a-rectangular-magnetic-core\/","title":{"rendered":"A rectangular magnetic core"},"content":{"rendered":"\n

A rectangular magnetic core shown in Fig. 8.21 has square cross section of area 16 cm2. An air gap of 2 mm is cut across one of its limbs. Find the exciting current needed in the coil having 1,000 turns wound on the core to create an air-gap flux of 4 mWb. The relative permeability of the core is 2000.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n

Answer:<\/h3>\n\n\n\n

The exciting current required in the coil is 4.97 A<\/strong>.<\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

To determine the exciting current required to establish an air-gap flux of 4 mWb<\/strong> in a rectangular magnetic core with a square cross-section, we follow these steps:<\/p>\n\n\n\n

    \n
  1. Understanding the Magnetic Circuit<\/strong>:
    The core has a square cross-section of 16 cm\u00b2<\/strong>, and an air gap of 2 mm<\/strong> is introduced. The presence of the air gap significantly increases the reluctance in the magnetic circuit. The coil wrapped around the core has 1,000 turns<\/strong>, and the relative permeability of the core is given as 2000<\/strong>.<\/li>\n\n\n\n
  2. Calculating Reluctances<\/strong>:
    Magnetic reluctance (( R )) is analogous to electrical resistance in an electrical circuit and is given by: [
    R = \\frac{l}{\\mu A}
    ] where:<\/li>\n<\/ol>\n\n\n\n
      \n
    • ( l ) is the length of the magnetic path,<\/li>\n\n\n\n
    • ( \\mu ) is the permeability ((\\mu_0 \\mu_r) for the core and (\\mu_0) for the air gap),<\/li>\n\n\n\n
    • ( A ) is the cross-sectional area.<\/li>\n\n\n\n
    • Reluctance of the Air Gap<\/strong>: The permeability of free space is ( \\mu_0 = 4\\pi \\times 10^{-7} ) H\/m.
      The reluctance of the air gap is calculated as: [
      R_g = \\frac{l_g}{\\mu_0 A}
      ]<\/li>\n\n\n\n
    • Reluctance of the Core<\/strong>:
      Assuming a rectangular shape of the core with 20 cm \u00d7 30 cm<\/strong> outer dimensions, the mean magnetic path length is: [
      l_c = 2 \\times (0.2 + 0.3) = 1 \\text{ m}
      ] The core permeability is: [
      \\mu = \\mu_r \\times \\mu_0
      ] So, the reluctance of the core is: [
      R_c = \\frac{l_c}{\\mu A}
      ]<\/li>\n\n\n\n
    • Total Reluctance<\/strong>: [
      R_{total} = R_g + R_c
      ]<\/li>\n<\/ul>\n\n\n\n
        \n
      1. Finding MMF (Magnetomotive Force)<\/strong>:
        The MMF required to drive the magnetic flux is: [
        \\text{MMF} = \\Phi \\times R_{total}
        ]<\/li>\n\n\n\n
      2. Determining the Exciting Current<\/strong>:
        Since MMF is given by: [
        \\text{MMF} = N I
        ] Solving for ( I )<\/strong>: [
        I = \\frac{\\text{MMF}}{N}
        ] Substituting values, the required exciting current is 4.97 A<\/strong>.<\/li>\n<\/ol>\n\n\n\n

        This current ensures that the desired flux of 4 mWb<\/strong> is established across the air gap.<\/p>\n","protected":false},"excerpt":{"rendered":"

        A rectangular magnetic core shown in Fig. 8.21 has square cross section of area 16 cm2. An air gap of 2 mm is cut across one of its limbs. Find the exciting current needed in the coil having 1,000 turns wound on the core to create an air-gap flux of 4 mWb. The relative permeability […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-190989","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/190989","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=190989"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/190989\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=190989"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=190989"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=190989"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}