{"id":43667,"date":"2025-06-30T08:58:27","date_gmt":"2025-06-30T08:58:27","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=43667"},"modified":"2025-06-30T08:58:33","modified_gmt":"2025-06-30T08:58:33","slug":"two-14-cm-diameter-electrodes-0-46-cm-apart-form-a-parallel-plate-capacitor","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/two-14-cm-diameter-electrodes-0-46-cm-apart-form-a-parallel-plate-capacitor\/","title":{"rendered":"Two 14-cm-diameter electrodes 0.46 cm apart form a parallel-plate capacitor"},"content":{"rendered":"\n<p>Two 14-cm-diameter electrodes 0.46 cm apart form a parallel-plate capacitor. The electrodes are attached by metal wires to the terminals of a 18 V battery.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To calculate the capacitance of a parallel-plate capacitor, the formula is given by: C=\u03b50\u22c5AdC = \\frac{\\varepsilon_0 \\cdot A}{d}<\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>CC is the capacitance in farads (F),<\/li>\n\n\n\n<li>\u03b50\\varepsilon_0 is the vacuum permittivity (8.85\u00d710\u221212\u2009F\/m8.85 \\times 10^{-12} \\, \\text{F\/m}),<\/li>\n\n\n\n<li>AA is the area of the plate in square meters (m\u00b2),<\/li>\n\n\n\n<li>dd is the separation between the plates in meters (m).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Calculate the area of the electrode<\/h3>\n\n\n\n<p>The electrodes are circular, so the area AA of one electrode is calculated using the formula for the area of a circle: A=\u03c0r2A = \\pi r^2<\/p>\n\n\n\n<p>The diameter of each electrode is given as 14 cm, so the radius rr is half of that: r=14\u2009cm2=7\u2009cm=0.07\u2009mr = \\frac{14 \\, \\text{cm}}{2} = 7 \\, \\text{cm} = 0.07 \\, \\text{m}<\/p>\n\n\n\n<p>Now, calculate the area: A=\u03c0\u00d7(0.07)2=\u03c0\u00d70.0049\u2009m2\u22480.0154\u2009m2A = \\pi \\times (0.07)^2 = \\pi \\times 0.0049 \\, \\text{m}^2 \\approx 0.0154 \\, \\text{m}^2<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Convert the separation distance between the plates<\/h3>\n\n\n\n<p>The separation between the plates is 0.46 cm, which needs to be converted to meters: d=0.46\u2009cm=0.0046\u2009md = 0.46 \\, \\text{cm} = 0.0046 \\, \\text{m}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Calculate the capacitance<\/h3>\n\n\n\n<p>Substitute the values of \u03b50\\varepsilon_0, AA, and dd into the capacitance formula: C=(8.85\u00d710\u221212)\u00d70.01540.0046C = \\frac{(8.85 \\times 10^{-12}) \\times 0.0154}{0.0046} C\u22481.36\u00d710\u2212130.0046\u22482.96\u00d710\u221211\u2009FC \\approx \\frac{1.36 \\times 10^{-13}}{0.0046} \\approx 2.96 \\times 10^{-11} \\, \\text{F}<\/p>\n\n\n\n<p>Thus, the capacitance of the parallel-plate capacitor is approximately 2.96\u00d710\u2212112.96 \\times 10^{-11} farads or 29.6 picofarads (pF).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Determine the charge on the capacitor<\/h3>\n\n\n\n<p>The charge stored on the capacitor can be calculated using the formula: Q=C\u22c5VQ = C \\cdot V<\/p>\n\n\n\n<p>where VV is the voltage across the capacitor, which is 18 V. Substituting the values: Q=(2.96\u00d710\u221211\u2009F)\u00d7(18\u2009V)=5.33\u00d710\u221210\u2009CQ = (2.96 \\times 10^{-11} \\, \\text{F}) \\times (18 \\, \\text{V}) = 5.33 \\times 10^{-10} \\, \\text{C}<\/p>\n\n\n\n<p>Thus, the charge stored on the capacitor is approximately 5.33\u00d710\u2212105.33 \\times 10^{-10} coulombs or 533 nanocoulombs (nC).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Two 14-cm-diameter electrodes 0.46 cm apart form a parallel-plate capacitor. The electrodes are attached by metal wires to the terminals of a 18 V battery. The correct answer and explanation is: To calculate the capacitance of a parallel-plate capacitor, the formula is given by: C=\u03b50\u22c5AdC = \\frac{\\varepsilon_0 \\cdot A}{d} where: Step 1: Calculate the area [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-43667","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/43667","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=43667"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/43667\/revisions"}],"predecessor-version":[{"id":43668,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/43667\/revisions\/43668"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=43667"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=43667"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=43667"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}