{"id":1629,"date":"2018-03-28T12:26:17","date_gmt":"2018-03-28T04:26:17","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=1629"},"modified":"2023-08-10T00:47:20","modified_gmt":"2023-08-10T00:47:20","slug":"kirchhoffs-first-rule-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/kirchhoffs-first-rule-problems-and-solutions.htm","title":{"rendered":"Kirchhoffs first rule \u2013 problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"<p style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">Kirchhoffs first rule \u2013 problems and solutions<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">1. Based on figure as shown below, if I<sub>1<\/sub> = 5A, I<sub>2<\/sub> = 3 A, I<sub>3<\/sub> = 6 A, then I<sub>4 <\/sub>= \u2026&#8230;&#8230;<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignright size-full wp-image-1630\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/03\/Kirchhoff\u2019s-first-rule-\u2013-problems-and-solutions-1.png\" alt=\"Kirchhoff\u2019s first rule \u2013 problems and solutions 1\" width=\"151\" height=\"138\" \/>Solution :<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><a href=\"https:\/\/gurumuda.net\/physics\/kirchhoffs-first-rule-problems-and-solutions.htm\" target=\"_blank\" rel=\"noopener\">Kirchhoff\u2019s first rule<\/a> states that the sums of all currents entering the junction must equal the sum of all currents leaving the junction. <\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">I<sub>1 <\/sub>and I<sub>2 <\/sub>are entering the junction, whereas I<sub>3<\/sub> and I<sub>4 <\/sub>are leaving.<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">Apply Kirchhoff\u2019s first rule :<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">I<sub>1<\/sub> + I<sub>2 <\/sub>= I<sub>3<\/sub> + I<sub>4<\/sub><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">5 + 3 = 6 + I<sub>4<\/sub><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">8 = 6 + I<sub>4<\/sub><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">I<sub>4<\/sub> = 8 \u2013 6<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">I<sub>4<\/sub> = 2 Ampere<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">2. If I<sub>1<\/sub> = I<sub>3<\/sub> then I<sub>4<\/sub> =\u2026&#8230;..<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><u><img loading=\"lazy\" decoding=\"async\" class=\"alignright size-full wp-image-1631\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/03\/Kirchhoff\u2019s-first-rule-\u2013-problems-and-solutions-2.png\" alt=\"Kirchhoff\u2019s first rule \u2013 problems and solutions 2\" width=\"186\" height=\"157\" \/>Known :<\/u><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">I<sub>1 <\/sub>= I<sub>3<\/sub> = 2 Ampere<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">I<sub>2<\/sub> = 3 Ampere<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">I<sub>5 <\/sub>= 4 Ampere<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><u>Wanted:<\/u> I<sub>4<\/sub><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><u>Solution :<\/u><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">I<sub>1 <\/sub>and I<sub>4 <\/sub>are entering the junction, whereas I<sub>2<\/sub>, I<sub>3<\/sub>, and I<sub>5 <\/sub>are leaving.<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">Apply Kirchhoff\u2019s first rule :<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">I<sub>1<\/sub> + I<sub>4 <\/sub>= I<sub>2<\/sub> + I<sub>3 <\/sub>+ I<sub>5<\/sub><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">2 + I<sub>4 <\/sub>= 3 + 2 + 4<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">2 + I<sub>4 <\/sub>= 9<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">I<sub>4 <\/sub>= 9 \u2013 2 <\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">I<sub>4<\/sub> = 7 Ampere <\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">3. I<sub>1<\/sub> = \u2026&#8230;.<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">Solution :<img loading=\"lazy\" decoding=\"async\" class=\"alignright size-full wp-image-1632\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/03\/Kirchhoff\u2019s-first-rule-\u2013-problems-and-solutions-3.png\" alt=\"Kirchhoff\u2019s first rule \u2013 problems and solutions 3\" width=\"149\" height=\"91\" \/><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">I am entering the junction, whereas I<sub>1<\/sub>, I<sub>2<\/sub>, and I<sub>3<\/sub> are leaving.<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">Apply Kirchhoff\u2019s first rule :<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">I = I<sub>1<\/sub> + I<sub>2 <\/sub>+ I<sub>3<\/sub><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">7 A = I<sub>1<\/sub> + 1 A + 4 A<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">7 A = I<sub>1<\/sub> + 5 A <\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">7 A &#8211; 5 A = I<sub>1<\/sub><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">I<sub>1 <\/sub>= 2 Ampere<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">4. I<sub>2<\/sub> = \u2026&#8230;&#8230;<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><u>Wanted:<\/u> I<sub>2<img loading=\"lazy\" decoding=\"async\" class=\"alignright size-full wp-image-1633\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/03\/Kirchhoff\u2019s-first-rule-\u2013-problems-and-solutions-4.png\" alt=\"Kirchhoff\u2019s first rule \u2013 problems and solutions 4\" width=\"224\" height=\"90\" \/><\/sub><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><u>Solution :<\/u><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">I<sub>1 <\/sub>is entering the junction, whereas I<sub>2,<\/sub> I<sub>3, <\/sub>and I<sub>4<\/sub> are leaving.<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">Apply Kirchhoff\u2019s first rule :<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">I<sub>1<\/sub> = I<sub>2<\/sub> + I<sub>3<\/sub> + I<sub>4<\/sub><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">6 = I<sub>2<\/sub> + 3 + 1<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">6 = I<sub>2<\/sub> + 4<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">I<sub>2 <\/sub>= 6 \u2013 4<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">I<sub>2<\/sub> = 2 Ampere<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">5. If I<sub>2<\/sub> = 1\/4 I<sub>1<\/sub> , then I<sub>3<\/sub> = \u2026&#8230;&#8230;<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><u>Known :<img loading=\"lazy\" decoding=\"async\" class=\"alignright size-full wp-image-1634\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/03\/Kirchhoff\u2019s-first-rule-\u2013-problems-and-solutions-5.png\" alt=\"Kirchhoff\u2019s first rule \u2013 problems and solutions 5\" width=\"213\" height=\"106\" \/><\/u><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">I<sub>1<\/sub> = 600 milliAmpere<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><u>Wanted:<\/u> I<sub>3<\/sub><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\"><u>Solution :<\/u><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">I<sub>2<\/sub> = 1\/4 I<sub>1 <\/sub>= 1\/4 (600 mA) = 150 mA<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">I<sub>1 <\/sub>is entering the junction, whereas I<sub>2<\/sub> and I<sub>3<\/sub> are leaving.<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">Apply Kirchhoff\u2019s first rule :<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">I<sub>1<\/sub> = I<sub>2<\/sub> + I<sub>3<\/sub><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">600 mA = 150 mA + I<sub>3<\/sub><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">I<sub>3<\/sub> = 600 mA &#8211; 150 mA<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">I<sub>3<\/sub> = 450 mA<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">6. Based on figure below, find I!<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">Solution :<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">Apply Kirchhoff&#8217;s first rule :<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">3 + 5 + 2 = 7 + I<img loading=\"lazy\" decoding=\"async\" class=\"alignright size-full wp-image-2865\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/03\/Kirchhoff\u2019s-first-rule-\u2013-problems-and-solutions-10.png\" alt=\"Kirchhoff\u2019s first rule \u2013 problems and solutions 10\" width=\"206\" height=\"176\" \/><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">10 = 7 + I<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">10 \u2013 7 = I<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">I = 3 Ampere<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">7. Based on figure below, if I<sub>1<\/sub> = 4 A, I<sub>2<\/sub> = 3 A, I<sub>4<\/sub> = 7 A, I<sub>5<\/sub> = 4 A, determine I<sub>3<\/sub>.<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-family: 'times new roman', times, serif; font-size: 12pt;\">Solution :<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><i>Electric current entering the junction<\/i><i> = I<\/i><sub><i>1 <\/i><\/sub><i>+ I<\/i><sub><i>3 <\/i><\/sub><i>= 4 A + I<\/i><sub><i>3<\/i><\/sub><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><i>Electric current leaving the junction <\/i><i>= I<\/i><sub><i>2 <\/i><\/sub><i>+ I<\/i><sub><i>4 <\/i><\/sub><i>+ I<\/i><sub><i>5<\/i><\/sub><i> = 3 A + 7 A + 4 A = 14 A<img loading=\"lazy\" decoding=\"async\" class=\"alignright size-full wp-image-2866\" src=\"https:\/\/gurumuda.net\/physics\/wp-content\/uploads\/2018\/03\/Kirchhoff\u2019s-first-rule-\u2013-problems-and-solutions-11.png\" alt=\"Kirchhoff\u2019s first rule \u2013 problems and solutions 11\" width=\"157\" height=\"161\" \/><\/i><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">14 A = 4 A + I<sub>3<\/sub><\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">I<sub>3<\/sub> = 14 A \u2013 4 A<\/span><\/p>\n<p class=\"western\" style=\"text-align: justify;\" align=\"justify\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\">I<sub>3<\/sub> = 10 A<\/span><\/p>\n<ol style=\"text-align: justify;\">\n<li><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>What is the primary principle behind Kirchhoff&#8217;s First Rule?<\/strong><\/span>\n<ul>\n<li><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>Answer<\/strong>: The primary principle behind Kirchhoff&#8217;s First Rule is the conservation of electric charge. It implies that no charge is lost at any node or junction in a circuit.<\/span><\/li>\n<\/ul>\n<\/li>\n<li><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>If three currents, <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">I<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><sub><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/sub><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">I<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><sub><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/sub><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, and <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">I<\/span><sub><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/sub><\/span><\/span><\/span><\/span><\/span>, converge on a node and <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">I<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><sub><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/sub><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> is entering while <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">I<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><sub><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/sub><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> and <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">I<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><sub><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/sub><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> are leaving, how is KCL expressed for this node?<\/strong><\/span>\n<ul>\n<li><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>Answer<\/strong>: According to KCL, <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">I<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><sub><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/sub><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">I<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><sub><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/sub><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">I<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><sub><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/sub><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/span><\/li>\n<\/ul>\n<\/li>\n<li><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>Why is KCL important in the analysis of electrical circuits?<\/strong><\/span>\n<ul>\n<li><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>Answer<\/strong>: KCL provides a fundamental constraint that any valid solution to a circuit problem must satisfy, ensuring that the behavior of currents in a network adheres to the conservation of charge principle.<\/span><\/li>\n<\/ul>\n<\/li>\n<li><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>Is KCL valid only for DC circuits or also for AC circuits?<\/strong><\/span>\n<ul>\n<li><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>Answer<\/strong>: KCL is valid for both DC and AC circuits. It is a reflection of the conservation of charge, which is universal, regardless of how the currents change over time.<\/span><\/li>\n<\/ul>\n<\/li>\n<li><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>In a circuit with several nodes, is it necessary to apply KCL to every node to analyze the circuit fully?<\/strong><\/span>\n<ul>\n<li><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>Answer<\/strong>: Not always. While you can apply KCL to every node, often analyzing a subset of nodes is sufficient to determine the behavior of the entire circuit.<\/span><\/li>\n<\/ul>\n<\/li>\n<li><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>How does the concept of a &#8220;ground&#8221; or reference node in a circuit relate to KCL?<\/strong><\/span>\n<ul>\n<li><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>Answer<\/strong>: A ground or reference node serves as a common point of reference for voltages in the circuit. Applying KCL to this node, like any other node, ensures that the sum of currents is zero. Ground doesn&#8217;t affect the applicability or the outcome of KCL.<\/span><\/li>\n<\/ul>\n<\/li>\n<li><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>If a node has only two branches connected to it, and the current in one branch is known, is it necessary to solve for the current in the other branch using KCL?<\/strong><\/span>\n<ul>\n<li><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>Answer<\/strong>: No, if the current in one branch is known and there are only two branches connected to the node, the current in the other branch is simply the negative of the known current (indicating it&#8217;s in the opposite direction).<\/span><\/li>\n<\/ul>\n<\/li>\n<li><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>How does the behavior of capacitors in a circuit relate to KCL?<\/strong><\/span>\n<ul>\n<li><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>Answer<\/strong>: While capacitors can store charge, the rate of charge entering a capacitor is equal to the rate of charge leaving its other terminal. Therefore, even with capacitors, the net current at a node (including a node at one terminal of the capacitor) is zero, and KCL remains valid.<\/span><\/li>\n<\/ul>\n<\/li>\n<li><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>In practical circuits with real components, does KCL hold perfectly, or are there any exceptions?<\/strong><\/span>\n<ul>\n<li><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>Answer<\/strong>: In ideal circuit analysis, KCL holds perfectly. In real-world situations, components might have tiny leakage currents or parasitic effects, but for most practical purposes and analyses, KCL is assumed to hold true.<\/span><\/li>\n<\/ul>\n<\/li>\n<li><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>When might one use both Kirchhoff&#8217;s First (Current) Rule and Second (Voltage) Rule in analyzing a circuit?<\/strong><\/span><\/li>\n<\/ol>\n<ul>\n<li style=\"text-align: justify;\"><span style=\"font-size: 12pt; font-family: 'times new roman', times, serif;\"><strong>Answer<\/strong>: In many complex circuits, especially those with multiple loops and nodes, both KCL (First Rule) and Kirchhoff&#8217;s Voltage Law (Second Rule) are used together to set up a system of equations that can then be solved to determine unknown currents and voltages throughout the circuit.<\/span><\/li>\n<\/ul>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"<p>Kirchhoffs first rule \u2013 problems and solutions 1. Based on figure as shown below, if I1 = 5A, I2 = 3 A, I3 = 6 A, then I4 = \u2026&#8230;&#8230; Solution : Kirchhoff\u2019s first rule states that the sums of all currents entering the junction must equal the sum of all currents leaving the junction. &#8230; <a title=\"Kirchhoffs first rule \u2013 problems and solutions\" class=\"read-more\" href=\"https:\/\/gurumuda.net\/physics\/kirchhoffs-first-rule-problems-and-solutions.htm\" aria-label=\"Read more about Kirchhoffs first rule \u2013 problems and solutions\">Read more<\/a><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_seopress_titles_title":"","_seopress_titles_desc":"","_seopress_robots_index":"","_seopress_robots_follow":"","_seopress_robots_imageindex":"","_seopress_robots_snippet":"","_seopress_robots_primary_cat":"","_seopress_robots_breadcrumbs":"","_seopress_robots_freeze_modified_date":"","_seopress_robots_custom_modified_date":"","_seopress_robots_canonical":"","_seopress_social_fb_title":"","_seopress_social_fb_desc":"","_seopress_social_fb_img":"","_seopress_social_fb_img_attachment_id":0,"_seopress_social_fb_img_width":0,"_seopress_social_fb_img_height":0,"_seopress_social_twitter_title":"","_seopress_social_twitter_desc":"","_seopress_social_twitter_img":"","_seopress_social_twitter_img_attachment_id":0,"_seopress_social_twitter_img_width":0,"_seopress_social_twitter_img_height":0,"_seopress_redirections_value":"","_seopress_redirections_enabled":"","_seopress_redirections_enabled_regex":"","_seopress_redirections_logged_status":"","_seopress_redirections_param":"","_seopress_redirections_type":0,"_seopress_analysis_target_kw":"Kirchhoffs first rule \u2013 problems and solutions","_seopress_news_disabled":"","_seopress_video_disabled":"","_seopress_video":[],"_seopress_pro_schemas_manual":[],"_seopress_pro_rich_snippets_disable_all":"","_seopress_pro_rich_snippets_disable":[],"_seopress_pro_schemas":[],"footnotes":""},"categories":[3],"tags":[],"class_list":["post-1629","post","type-post","status-publish","format-standard","hentry","category-solved-problems-in-basic-physics"],"gt_translate_keys":[{"key":"link","format":"url"}],"_links":{"self":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/1629","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/comments?post=1629"}],"version-history":[{"count":2,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/1629\/revisions"}],"predecessor-version":[{"id":8739,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/1629\/revisions\/8739"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=1629"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=1629"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=1629"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}