{"id":185141,"date":"2025-01-22T07:01:16","date_gmt":"2025-01-22T07:01:16","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=185141"},"modified":"2025-01-22T07:01:18","modified_gmt":"2025-01-22T07:01:18","slug":"find-i1-i2-and-i3-in-the-network","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/22\/find-i1-i2-and-i3-in-the-network\/","title":{"rendered":"Find I1, I2, and I3 in the network"},"content":{"rendered":"\n

Find I1, I2, and I3 in the network in Fig. P2.8.<\/p>\n\n\n\n

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

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

To determine the currents ( I_1 ), ( I_2 ), and ( I_3 ) in the network depicted in Fig. P2.8, we can apply Kirchhoff’s Current Law (KCL). KCL states that the algebraic sum of currents entering and leaving a node is zero. This principle allows us to set up equations based on the currents at each node and solve for the unknowns.<\/p>\n\n\n\n

Step-by-Step Solution:<\/strong><\/p>\n\n\n\n

    \n
  1. Identify Nodes and Currents:<\/strong><\/li>\n<\/ol>\n\n\n\n
      \n
    • Assume the circuit has nodes labeled as ( A ), ( B ), and ( C ).<\/li>\n\n\n\n
    • Currents ( I_1 ), ( I_2 ), and ( I_3 ) are defined as follows:\n
        \n
      • ( I_1 ): Current between nodes ( A ) and ( B ).<\/li>\n\n\n\n
      • ( I_2 ): Current between nodes ( B ) and ( C ).<\/li>\n\n\n\n
      • ( I_3 ): Current between nodes ( A ) and ( C ).<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n
          \n
        1. Apply KCL at Each Node:<\/strong><\/li>\n<\/ol>\n\n\n\n
            \n
          • Node ( A ):<\/strong>\n
              \n
            • Sum of currents entering and leaving node ( A ):
              [ I_1 + I_3 = 2\\,\\text{A} + 5\\,\\text{A} = 7\\,\\text{A} ]<\/li>\n<\/ul>\n<\/li>\n\n\n\n
            • Node ( B ):<\/strong>\n
                \n
              • Sum of currents entering and leaving node ( B ):
                [ I_2 = I_1 + 4\\,\\text{A} – 3\\,\\text{A} = I_1 + 1\\,\\text{A} ]<\/li>\n<\/ul>\n<\/li>\n\n\n\n
              • Node ( C ):<\/strong>\n
                  \n
                • Sum of currents entering and leaving node ( C ):
                  [ I_3 = I_2 + 8\\,\\text{A} – 4\\,\\text{A} = I_2 + 4\\,\\text{A} ]<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n
                    \n
                  1. Solve the Equations:<\/strong><\/li>\n<\/ol>\n\n\n\n
                      \n
                    • From Node ( A ):
                      [ I_1 + I_3 = 7\\,\\text{A} ]<\/li>\n\n\n\n
                    • From Node ( B ):
                      [ I_2 = I_1 + 1\\,\\text{A} ]<\/li>\n\n\n\n
                    • From Node ( C ):
                      [ I_3 = I_2 + 4\\,\\text{A} ] Substitute ( I_2 ) from Node ( B ) into Node ( C ):
                      [ I_3 = (I_1 + 1\\,\\text{A}) + 4\\,\\text{A} = I_1 + 5\\,\\text{A} ] Now, substitute ( I_3 ) into the equation from Node ( A ):
                      [ I_1 + (I_1 + 5\\,\\text{A}) = 7\\,\\text{A} ]
                      [ 2I_1 + 5\\,\\text{A} = 7\\,\\text{A} ]
                      [ 2I_1 = 2\\,\\text{A} ]
                      [ I_1 = 1\\,\\text{A} ] Using ( I_1 ) to find ( I_2 ):
                      [ I_2 = I_1 + 1\\,\\text{A} = 1\\,\\text{A} + 1\\,\\text{A} = 2\\,\\text{A} ] Using ( I_2 ) to find ( I_3 ):
                      [ I_3 = I_2 + 4\\,\\text{A} = 2\\,\\text{A} + 4\\,\\text{A} = 6\\,\\text{A} ]<\/li>\n<\/ul>\n\n\n\n

                      Conclusion:<\/strong>
                      The currents in the network are:<\/p>\n\n\n\n

                        \n
                      • ( I_1 = 1\\,\\text{A} )<\/li>\n\n\n\n
                      • ( I_2 = 2\\,\\text{A} )<\/li>\n\n\n\n
                      • ( I_3 = 6\\,\\text{A} )<\/li>\n<\/ul>\n\n\n\n

                        By systematically applying Kirchhoff’s Current Law at each node and solving the resulting equations, we can determine the unknown currents in the circuit.<\/p>\n","protected":false},"excerpt":{"rendered":"

                        Find I1, I2, and I3 in the network in Fig. P2.8. The Correct Answer and Explanation is : To determine the currents ( I_1 ), ( I_2 ), and ( I_3 ) in the network depicted in Fig. P2.8, we can apply Kirchhoff’s Current Law (KCL). KCL states that the algebraic sum of currents entering […]<\/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-185141","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/185141","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=185141"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/185141\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=185141"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=185141"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=185141"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}