{"id":228391,"date":"2025-06-07T08:57:02","date_gmt":"2025-06-07T08:57:02","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=228391"},"modified":"2025-06-07T08:57:04","modified_gmt":"2025-06-07T08:57:04","slug":"a-circuit-is-constructed-with-four-resistors-one-inductor-one-battery-and-a-switch-as-shown","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/07\/a-circuit-is-constructed-with-four-resistors-one-inductor-one-battery-and-a-switch-as-shown\/","title":{"rendered":"A circuit is constructed with four resistors, one inductor, one battery, and a switch as shown."},"content":{"rendered":"\n

A circuit is constructed with four resistors, one inductor, one battery, and a switch as shown. The values for the resistors are: R1 = 770\u00ce\u00a9, R2 = 660\u00ce\u00a9, and R4 = 102\u00ce\u00a9. The inductance is L = 635 mH and the battery voltage is V = 24V.
A circuit is constructed with four resistors, one inductor, one battery, and a switch as shown. The values for the resistors are: R1 = 770\u00ce\u00a9, R2 = 660\u00ce\u00a9, and R4 = 102\u00ce\u00a9. The inductance is L = 635 mH and the battery voltage is V = 24V.<\/p>\n\n\n\n

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

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

Given Values:<\/strong><\/h3>\n\n\n\n
    \n
  • Resistors:\n
      \n
    • R1=R2=77\u2009\u03a9R_1 = R_2 = 77\\,\\OmegaR1\u200b=R2\u200b=77\u03a9<\/li>\n\n\n\n
    • R3=66\u2009\u03a9R_3 = 66\\,\\OmegaR3\u200b=66\u03a9<\/li>\n\n\n\n
    • R4=102\u2009\u03a9R_4 = 102\\,\\OmegaR4\u200b=102\u03a9<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • Inductance: L=635\u2009mH=0.635\u2009HL = 635\\,\\text{mH} = 0.635\\,\\text{H}L=635mH=0.635H<\/li>\n\n\n\n
    • Battery voltage: V=24\u2009VV = 24\\,\\text{V}V=24V<\/li>\n<\/ul>\n\n\n\n
      \n\n\n\n

      Circuit Configuration:<\/strong><\/h3>\n\n\n\n

      From the image:<\/p>\n\n\n\n

        \n
      • R1R_1R1\u200b and R2R_2R2\u200b are in series in the top branch with the inductor LLL between them.<\/li>\n\n\n\n
      • R3R_3R3\u200b and R4R_4R4\u200b are in the lower loop, also forming a branch when the switch is closed.<\/li>\n\n\n\n
      • The battery supplies the entire circuit, and the switch controls the connection of the bottom branch.<\/li>\n<\/ul>\n\n\n\n
        \n\n\n\n

        Analysis Immediately After Switch is Closed (t = 0):<\/strong><\/h3>\n\n\n\n

        At t=0t = 0t=0, the inductor behaves like an open circuit<\/strong> (because inductors resist a change in current). Therefore, no current flows through the inductor branch<\/strong> (i.e., through R1R_1R1\u200b, LLL, and R2R_2R2\u200b).<\/p>\n\n\n\n

        So, the current only flows through the bottom branch: R4R_4R4\u200b and R3R_3R3\u200b, in series. Req (t=0)=R4+R3=102\u2009\u03a9+66\u2009\u03a9=168\u2009\u03a9R_{\\text{eq (t=0)}} = R_4 + R_3 = 102\\,\\Omega + 66\\,\\Omega = 168\\,\\OmegaReq (t=0)\u200b=R4\u200b+R3\u200b=102\u03a9+66\u03a9=168\u03a9 Iinitial=VReq=24\u2009V168\u2009\u03a9\u22480.143\u2009AI_{\\text{initial}} = \\frac{V}{R_{\\text{eq}}} = \\frac{24\\,\\text{V}}{168\\,\\Omega} \\approx 0.143\\,\\text{A}Iinitial\u200b=Req\u200bV\u200b=168\u03a924V\u200b\u22480.143A<\/p>\n\n\n\n

        \n\n\n\n

        After a Long Time (t \u2192 \u221e):<\/strong><\/h3>\n\n\n\n

        After a long time, the inductor behaves like a short circuit<\/strong> (acts like a wire). So now current can flow through the inductor branch and the bottom branch.<\/p>\n\n\n\n

          \n
        • Top branch resistance: R1+R2=77+77=154\u2009\u03a9R_1 + R_2 = 77 + 77 = 154\\,\\OmegaR1\u200b+R2\u200b=77+77=154\u03a9<\/li>\n\n\n\n
        • Bottom branch resistance: R3+R4=66+102=168\u2009\u03a9R_3 + R_4 = 66 + 102 = 168\\,\\OmegaR3\u200b+R4\u200b=66+102=168\u03a9<\/li>\n<\/ul>\n\n\n\n

          These two branches are in parallel<\/strong>, so we compute the equivalent resistance: 1Req=1154+1168\u21d2Req\u224880.0\u2009\u03a9\\frac{1}{R_{\\text{eq}}} = \\frac{1}{154} + \\frac{1}{168} \\Rightarrow R_{\\text{eq}} \\approx 80.0\\,\\OmegaReq\u200b1\u200b=1541\u200b+1681\u200b\u21d2Req\u200b\u224880.0\u03a9 Ifinal=24\u2009V80\u2009\u03a9=0.30\u2009AI_{\\text{final}} = \\frac{24\\,\\text{V}}{80\\,\\Omega} = 0.30\\,\\text{A}Ifinal\u200b=80\u03a924V\u200b=0.30A<\/p>\n\n\n\n

          \n\n\n\n

          Conclusion:<\/strong><\/h3>\n\n\n\n
            \n
          • Initial current (t = 0):<\/strong> ~0.143 A (only through R3R_3R3\u200b and R4R_4R4\u200b)<\/li>\n\n\n\n
          • Final current (t \u2192 \u221e):<\/strong> ~0.30 A (distributed between two branches)<\/li>\n<\/ul>\n\n\n\n

            This demonstrates how inductors affect current flow over time, initially blocking and eventually allowing current.<\/p>\n\n\n\n

            \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

            A circuit is constructed with four resistors, one inductor, one battery, and a switch as shown. The values for the resistors are: R1 = 770\u00ce\u00a9, R2 = 660\u00ce\u00a9, and R4 = 102\u00ce\u00a9. The inductance is L = 635 mH and the battery voltage is V = 24V.A circuit is constructed with four resistors, one inductor, […]<\/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-228391","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228391","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=228391"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228391\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=228391"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=228391"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=228391"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}