{"id":74410,"date":"2022-02-13T16:20:09","date_gmt":"2022-02-13T10:50:09","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=74410"},"modified":"2025-07-23T14:58:38","modified_gmt":"2025-07-23T09:28:38","slug":"important-questions-for-cbse-class-12-physics-electrostatic-potential","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-material\/important-questions\/cbse\/class-12\/physics-electrostatic-potential\/","title":{"rendered":"Important Questions for CBSE Class 12 Physics &#8211; Electrostatic Potential and Capacitance"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/study-material\/important-questions\/cbse\/class-12\/physics-electrostatic-potential\/#Important_Questions_with_Answers_for_CBSE_Class_12_Physics\" title=\"Important Questions with Answers for CBSE Class 12 Physics\">Important Questions with Answers for CBSE Class 12 Physics<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/study-material\/important-questions\/cbse\/class-12\/physics-electrostatic-potential\/#Very_Short_Answer_Questions_with_Answers_for_CBSE_Class_12_Physics\" title=\"Very Short Answer Questions with Answers for CBSE Class 12 Physics\">Very Short Answer Questions with Answers for CBSE Class 12 Physics<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Important_Questions_with_Answers_for_CBSE_Class_12_Physics\"><\/span>Important Questions with Answers for CBSE Class 12 Physics<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>1. What is <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/physics-mcqs\/class-12\/chapter-2-electrostatic-potential-and-capacitance\/\">electrostatic potential<\/a>?<\/strong><\/p>\n<p><strong>2. Define the potential energy of a system of charges.<\/strong><\/p>\n<p><strong>3. What is the relation between electric field and electrostatic potential?<\/strong><\/p>\n<p><strong>Answer<\/strong>: The electric field (<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>E<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">E<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">E<\/span><\/span><\/span>) is the negative gradient of the electrostatic potential (<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>V<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">V<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">V<\/span><\/span><\/span>), i.e.,<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>E<\/mi><mo>=<\/mo><mo>\u2212<\/mo><mi mathvariant=\"normal\">\u2207<\/mi><mi>V<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">E = &#8211; \\nabla V<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">E<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">\u2212<\/span><span class=\"mord\">\u2207<\/span><span class=\"mord mathnormal\">V<\/span><\/span><\/span>, or in terms of magnitude,<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>E<\/mi><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mrow><mi>d<\/mi><mi>V<\/mi><\/mrow><mrow><mi>d<\/mi><mi>r<\/mi><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">E = &#8211; \\frac{dV}{dr}<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">E<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">\u2212<\/span><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mord mathnormal mtight\">r<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mord mathnormal mtight\">V<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/p>\n<p><strong>4. Derive an expression for the potential due to a point charge.<\/strong><\/p>\n<p><strong>Answer<\/strong>: The electrostatic potential due to a point charge<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>Q<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">Q<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">Q<\/span><\/span><\/span> at a distance<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>r<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">r<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">r<\/span><\/span><\/span> from the charge is given by:<\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>V<\/mi><mo>=<\/mo><mfrac><mrow><mi>k<\/mi><mi>Q<\/mi><\/mrow><mi>r<\/mi><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">V = \\frac{kQ}{r}<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">V<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"mord mathnormal\">r<\/span><span class=\"mord mathnormal\">k<\/span><span class=\"mord mathnormal\">Q<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span> where<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>k<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">k<\/annotation><\/semantics><\/math>\n<p><strong>5. What is the concept of electric potential energy of a charge in an electric field?<\/strong><\/p>\n<p><strong>Answer<\/strong>: The potential energy<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>U<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">U<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">U<\/span><\/span><\/span> of a charge<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>q<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">q<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">q<\/span><\/span><\/span> in an electric field is given by<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>U<\/mi><mo>=<\/mo><mi>q<\/mi><mi>V<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">U = qV<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">U<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">q<\/span><span class=\"mord mathnormal\">V<\/span><\/span><\/span>, where<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>V<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">V<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">V<\/span><\/span><\/span> is the electric potential at the position of the charge.<\/p>\n<p><strong>6. Define capacitance.<\/strong><\/p>\n<p><strong>Answer<\/strong>: Capacitance is the ability of a body to store charge per unit potential difference, and it is given by the formula<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>C<\/mi><mo>=<\/mo><mfrac><mi>Q<\/mi><mi>V<\/mi><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">C = \\frac{Q}{V}<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">V<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">Q<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>, where<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>Q<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">Q<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">Q<\/span><\/span><\/span> is the charge and<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>V<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">V<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">V<\/span><\/span><\/span> is the potential difference.<\/p>\n<p><strong>7. Derive the formula for the capacitance of a parallel plate capacitor.<\/strong><\/p>\n<p><strong>Answer<\/strong>: The capacitance<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>C<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">C<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><\/span><\/span> of a parallel plate capacitor is given by:<\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>C<\/mi><mo>=<\/mo><msub><mi>\u03f5<\/mi><mn>0<\/mn><\/msub><mfrac><mi>A<\/mi><mi>d<\/mi><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">C = \\epsilon_0 \\frac{A}{d}<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">\u03f5<\/span><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\">0<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"mord mathnormal\">d<\/span><span class=\"mord mathnormal\">A<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span> where<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>A<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">A<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><\/span><\/span> is the area of one plate,<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>d<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">d<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">d<\/span><\/span><\/span> is the separation between the plates, and<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03f5<\/mi><mn>0<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">\\epsilon_0<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">\u03f5<\/span><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\">0<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span> is the permittivity of free space.<\/p>\n<p><strong>8. What is the energy stored in a capacitor?<\/strong><\/p>\n<p><strong>Answer<\/strong>: The energy stored in a capacitor is given by:<\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>U<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mi>C<\/mi><msup><mi>V<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">U = \\frac{1}{2} C V^2<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">U<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\">21<\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\">C<\/span><span class=\"mord\"><span class=\"mord mathnormal\">V<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> or equivalently,<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>U<\/mi><mo>=<\/mo><mfrac><msup><mi>Q<\/mi><mn>2<\/mn><\/msup><mrow><mn>2<\/mn><mi>C<\/mi><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">U = \\frac{Q^2}{2C}<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">U<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<span class=\"mord mathnormal mtight\">C<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">Q<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"sizing reset-size3 size1 mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>, where<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>C<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">C<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><\/span><\/span> is the capacitance and<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>V<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">V<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">V<\/span><\/span><\/span> is the potential difference.<\/p>\n<p><strong>9. How does a dielectric material affect the capacitance of a capacitor?<\/strong><\/p>\n<p><strong>Answer<\/strong>: When a dielectric material is inserted between the plates of a capacitor, it increases the capacitance by a factor of the dielectric constant<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>k<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">k<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">k<\/span><\/span><\/span>, so the new capacitance is<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>C<\/mi><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msup><mo>=<\/mo><mi>k<\/mi><mi>C<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">C&#8217; = kC<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">k<\/span><span class=\"mord mathnormal\">C<\/span><\/span><\/span>, where<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>C<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">C<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><\/span><\/span> is the capacitance without the dielectric.<\/p>\n<p><strong>10. Explain the concept of dielectric breakdown.<\/strong><\/p>\n<p><strong>Answer<\/strong>: Dielectric breakdown occurs when the electric field in the dielectric material exceeds a critical value, causing the dielectric to conduct and the capacitor to lose its ability to store charge.<\/p>\n<p><strong>11. What is the combination of capacitors in series? Derive the formula for total capacitance.<\/strong><\/p>\n<p><strong>Answer<\/strong>: When capacitors are connected in series, the total capacitance<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>C<\/mi><mi>t<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">C_t<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">C<\/span><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 mathnormal mtight\">t<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span> is given by:<\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mfrac><mn>1<\/mn><msub><mi>C<\/mi><mi>t<\/mi><\/msub><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><msub><mi>C<\/mi><mn>1<\/mn><\/msub><\/mfrac><mo>+<\/mo><mfrac><mn>1<\/mn><msub><mi>C<\/mi><mn>2<\/mn><\/msub><\/mfrac><mo>+<\/mo><mo>\u22ef<\/mo><mo>+<\/mo><mfrac><mn>1<\/mn><msub><mi>C<\/mi><mi>n<\/mi><\/msub><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{1}{C_t} = \\frac{1}{C_1} + \\frac{1}{C_2} + \\dots + \\frac{1}{C_n}<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"mord mathnormal\">C<\/span><span class=\"msupsub\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span>1<\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"mord mathnormal\">C<\/span><span class=\"msupsub\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span>1<\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"mord mathnormal\">C<\/span><span class=\"msupsub\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span>1<\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"minner\">\u22ef<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"mord mathnormal\">C<\/span><span class=\"msupsub\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span>1<\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><strong>12. What is the combination of capacitors in parallel? Derive the formula for total capacitance.<\/strong><\/p>\n<p><strong>Answer<\/strong>: When capacitors are connected in parallel, the total capacitance<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>C<\/mi><mi>t<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">C_t<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">C<\/span><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 mathnormal mtight\">t<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span> is the sum of the individual capacitances:<\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>C<\/mi><mi>t<\/mi><\/msub><mo>=<\/mo><msub><mi>C<\/mi><mn>1<\/mn><\/msub><mo>+<\/mo><msub><mi>C<\/mi><mn>2<\/mn><\/msub><mo>+<\/mo><mo>\u22ef<\/mo><mo>+<\/mo><msub><mi>C<\/mi><mi>n<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">C_t = C_1 + C_2 + \\dots + C_n<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">C<\/span><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 mathnormal mtight\">t<\/span><\/span><\/span><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\">C<\/span><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\">1<\/span><\/span><\/span><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\">C<\/span><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\">2<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"minner\">\u22ef<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">C<\/span><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 mathnormal mtight\">n<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><strong>13. What is the effect of a dielectric material on the electric field inside a capacitor?<\/strong><\/p>\n<p><strong>Answer<\/strong>: The presence of a dielectric material decreases the electric field inside the capacitor because it polarizes in the presence of the electric field and partially cancels it out, reducing the effective field.<\/p>\n<p><strong>14. Derive the expression for the energy stored in a capacitor when it is charged by a battery.<\/strong><\/p>\n<p><strong>Answer<\/strong>: The energy stored in a capacitor when charged by a battery is:<\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>U<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mi>C<\/mi><msup><mi>V<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">U = \\frac{1}{2} C V^2<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">U<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\">21<\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\">C<\/span><span class=\"mord\"><span class=\"mord mathnormal\">V<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> where<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>C<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">C<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><\/span><\/span> is the capacitance and<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>V<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">V<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">V<\/span><\/span><\/span> is the potential difference across the capacitor.<\/p>\n<p><strong>15. What is the relation between charge, capacitance, and potential difference?<\/strong><\/p>\n<p><strong>Answer<\/strong>: The relationship between charge<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>Q<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">Q<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">Q<\/span><\/span><\/span>, capacitance<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>C<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">C<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><\/span><\/span>, and potential difference<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>V<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">V<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">V<\/span><\/span><\/span> is given by the equation:<\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>Q<\/mi><mo>=<\/mo><mi>C<\/mi><mo>\u00d7<\/mo><mi>V<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">Q = C \\times V<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">Q<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">V<\/span><\/span><\/span><\/p>\n<p><strong>16. Question:<\/strong> How does the energy stored in a capacitor change when the distance between the plates is increased?<\/p>\n<p><strong>Answer:<\/strong><br \/>\nWhen the distance between the plates of a capacitor is increased, the capacitance decreases. Since the energy stored in a capacitor is given by the formula<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>U<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mi>C<\/mi><msup><mi>V<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">U = \\frac{1}{2} C V^2<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">U<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\">C<\/span><span class=\"mord\"><span class=\"mord mathnormal\">V<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, a decrease in capacitance leads to a decrease in the energy stored, provided the voltage remains constant.<\/p>\n<p><strong>17. Question:<\/strong> What is the effect of a dielectric material on the potential difference across the plates of a capacitor?<\/p>\n<p><strong>Answer:<\/strong><br \/>\nWhen a dielectric material is inserted between the plates of a capacitor, the potential difference across the plates decreases for a given amount of charge. This is because the dielectric reduces the electric field between the plates, thus lowering the voltage needed to store the same amount of charge.<\/p>\n<p><strong>18. Question:<\/strong> What is the dielectric constant, and how does it affect the capacitance of a capacitor?<\/p>\n<p><strong>Answer:<\/strong><br \/>\nThe dielectric constant<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>k<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">k<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">k<\/span><\/span><\/span> is a measure of a material\u2019s ability to reduce the electric field between the plates of a capacitor. The capacitance of a capacitor increases by a factor of<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>k<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">k<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">k<\/span><\/span><\/span> when a dielectric material is inserted between the plates. The new capacitance becomes<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>C<\/mi><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msup><mo>=<\/mo><mi>k<\/mi><mi>C<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">C&#8217; = kC<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">k<\/span><span class=\"mord mathnormal\">C<\/span><\/span><\/span>, where<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>C<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">C<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><\/span><\/span> is the capacitance without the dielectric.<\/p>\n<p><strong>19. Question:<\/strong> Derive the expression for the electric field between the plates of a parallel plate capacitor.<\/p>\n<p><strong>Answer:<\/strong><br \/>\nThe electric field<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>E<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">E<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">E<\/span><\/span><\/span> between the plates of a parallel plate capacitor is given by:<\/p>\n<p>&nbsp;<\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>E<\/mi><mo>=<\/mo><mfrac><mi>\u03c3<\/mi><msub><mi>\u03f5<\/mi><mn>0<\/mn><\/msub><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">E = \\frac{\\sigma}{\\epsilon_0}<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">E<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"mord mathnormal\">\u03f5<\/span><span class=\"msupsub\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"mord mathnormal\">\u03c3<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>where<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\u03c3<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\sigma<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">\u03c3<\/span><\/span><\/span> is the surface charge density (<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\u03c3<\/mi><mo>=<\/mo><mfrac><mi>Q<\/mi><mi>A<\/mi><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\sigma = \\frac{Q}{A}<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">\u03c3<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">A<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">Q<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>, where<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>Q<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">Q<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">Q<\/span><\/span><\/span> is the charge on each plate and<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>A<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">A<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><\/span><\/span> is the area of the plate), and<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03f5<\/mi><mn>0<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">\\epsilon_0<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">\u03f5<\/span><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\">0<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span> is the permittivity of free space.<\/p>\n<p>For a parallel plate capacitor, the electric field is uniform between the plates.<\/p>\n<p><strong>20. Question:<\/strong> What is the relationship between the potential energy and the charge on a capacitor?<\/p>\n<p><strong>Answer:<\/strong><br \/>\nThe potential energy<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>U<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">U<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">U<\/span><\/span><\/span> stored in a capacitor is related to the charge<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>Q<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">Q<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">Q<\/span><\/span><\/span> and the capacitance<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>C<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">C<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><\/span><\/span> by the equation:<\/p>\n<p>&nbsp;<\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>U<\/mi><mo>=<\/mo><mfrac><msup><mi>Q<\/mi><mn>2<\/mn><\/msup><mrow><mn>2<\/mn><mi>C<\/mi><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">U = \\frac{Q^2}{2C}<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">U<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\">2<span class=\"mord mathnormal\">C<\/span><span class=\"mord mathnormal\">Q<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>This shows that for a given capacitance, the energy stored increases as the charge on the capacitor increases.<\/p>\n<p><strong>21. Question:<\/strong> How do you calculate the total energy stored in a system of capacitors connected in parallel?<\/p>\n<p><strong>Answer:<\/strong><br \/>\nFor capacitors connected in parallel, the total energy stored in the system is the sum of the energies stored in each individual capacitor. If<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>C<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><msub><mi>C<\/mi><mn>2<\/mn><\/msub><mo separator=\"true\">,<\/mo><mo>\u2026<\/mo><mo separator=\"true\">,<\/mo><msub><mi>C<\/mi><mi>n<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">C_1, C_2, \\dots, C_n<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">C<\/span><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\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mord\"><span class=\"mord mathnormal\">C<\/span><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\">2<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"minner\">\u2026<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\"><span class=\"mord mathnormal\">C<\/span><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 mathnormal mtight\">n<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span> are the capacitances of the capacitors connected in parallel, the total energy is given by:<\/p>\n<p>&nbsp;<\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>U<\/mi><mtext>total<\/mtext><\/msub><mo>=<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><munderover><mo>\u2211<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><msub><mi>C<\/mi><mi>i<\/mi><\/msub><msup><mi>V<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">U_{\\text{total}} = \\frac{1}{2} \\sum_{i=1}^{n} C_i V^2<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">U<\/span><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\"><span class=\"mord text mtight\">total<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\">21<\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">=<\/span>1<\/span><\/span><span class=\"mop op-symbol large-op\">\u2211<\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">C<\/span><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 mathnormal mtight\">i<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">V<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>where<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>V<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">V<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">V<\/span><\/span><\/span> is the potential difference across each capacitor (since they are in parallel, all capacitors have the same voltage).<\/p>\n<p><strong>22. Question:<\/strong> What is the energy density of an electric field?<\/p>\n<p><strong>Answer:<\/strong><br \/>\nThe energy density<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>u<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">u<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">u<\/span><\/span><\/span> of an electric field is the energy stored per unit volume of the field and is given by the formula:<\/p>\n<p>&nbsp;<\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>u<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><msub><mi>\u03f5<\/mi><mn>0<\/mn><\/msub><msup><mi>E<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">u = \\frac{1}{2} \\epsilon_0 E^2<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">u<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\">21<\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03f5<\/span><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\">0<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>where<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>E<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">E<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">E<\/span><\/span><\/span> is the electric field and<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03f5<\/mi><mn>0<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">\\epsilon_0<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">\u03f5<\/span><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\">0<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span> is the permittivity of free space.<\/p>\n<p><strong>23. Question:<\/strong> How does the charge on a capacitor change when the dielectric constant is increased?<\/p>\n<p><strong>Answer:<\/strong><br \/>\nWhen the dielectric constant of the material between the plates of a capacitor is increased, the capacitance increases, and thus for a given potential difference, the <strong>charge<\/strong> stored on the capacitor increases. This is because the relationship between charge, capacitance, and voltage is<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>Q<\/mi><mo>=<\/mo><mi>C<\/mi><mo>\u00d7<\/mo><mi>V<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">Q = C \\times V<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">Q<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">V<\/span><\/span><\/span>, and an increase in capacitance leads to an increase in charge for the same voltage.<\/p>\n<p><strong>24. Question:<\/strong> What is the effect of increasing the voltage on the energy stored in a capacitor?<\/p>\n<p><strong>Answer:<\/strong><br \/>\nThe energy stored in a capacitor is proportional to the square of the voltage. As the voltage increases, the energy stored in the capacitor increases by a factor of<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>V<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">V^2<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">V<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>. The energy stored is given by:<\/p>\n<p>&nbsp;<\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>U<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mi>C<\/mi><msup><mi>V<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">U = \\frac{1}{2} C V^2<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">U<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\">21<\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\">C<\/span><span class=\"mord\"><span class=\"mord mathnormal\">V<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>So, doubling the voltage will increase the energy stored by a factor of four.<\/p>\n<p><strong>25. Question:<\/strong> What happens to the capacitance of a capacitor if it is disconnected from the battery and the dielectric material is inserted?<\/p>\n<p><strong>Answer:<\/strong><br \/>\nIf a capacitor is disconnected from the battery, the charge on the plates remains constant. When a dielectric material is inserted, the capacitance increases due to the dielectric constant<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>k<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">k<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">k<\/span><\/span><\/span>, but the potential difference across the plates decreases. Since the charge remains the same, the energy stored in the capacitor also changes accordingly.<\/p>\n<p><strong>26. Question:<\/strong> How does the energy stored in a capacitor change if the capacitor is charged by a constant current?<\/p>\n<p><strong>Answer:<\/strong><br \/>\nWhen a capacitor is charged by a constant current, the voltage across the capacitor increases linearly with time. The energy stored in the capacitor at any instant is given by:<\/p>\n<p>&nbsp;<\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>U<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mi>C<\/mi><msup><mi>V<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">U = \\frac{1}{2} C V^2<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">U<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\">21<\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\">C<\/span><span class=\"mord\"><span class=\"mord mathnormal\">V<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>Since the voltage increases with time, the energy stored also increases, and the rate of increase in energy depends on the current and the capacitance.<\/p>\n<p><strong>27. Question:<\/strong> What is the role of a capacitor in a circuit?<\/p>\n<p><strong>Answer:<\/strong><br \/>\nA capacitor stores electrical energy and can release it when needed. It is used in circuits to smooth out fluctuations in voltage, filter signals, store energy temporarily, and in timing applications. It can also block direct current (DC) while allowing alternating current (AC) to pass through.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Very_Short_Answer_Questions_with_Answers_for_CBSE_Class_12_Physics\"><\/span>Very Short Answer Questions with Answers for CBSE Class 12 Physics<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>1. What is electrostatic potential?<\/strong><\/p>\n<p><strong>Answer: <\/strong>Electrostatic potential is the work done in bringing a unit positive charge from infinity to a point in an electric field without acceleration.<\/p>\n<p><strong>2. What is capacitance?<\/strong><\/p>\n<p><strong>Answer: <\/strong>Capacitance is the ability of a capacitor to store charge per unit potential difference, given by<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>C<\/mi><mo>=<\/mo><mfrac><mi>Q<\/mi><mi>V<\/mi><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">C = \\frac{Q}{V}<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">V<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">Q<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/p>\n<p><strong>3. What is the formula for the potential due to a point charge?<\/strong><\/p>\n<p><strong>Answer: <\/strong>The potential due to a point charge<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>Q<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">Q<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">Q<\/span><\/span><\/span> at a distance<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>r<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">r<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">r<\/span><\/span><\/span> is<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>V<\/mi><mo>=<\/mo><mfrac><mrow><mi>k<\/mi><mi>Q<\/mi><\/mrow><mi>r<\/mi><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">V = \\frac{kQ}{r}<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">V<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">r<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">k<\/span><span class=\"mord mathnormal mtight\">Q<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>, where<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>k<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">k<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">k<\/span><\/span><\/span> is Coulomb&#8217;s constant.<\/p>\n<p><strong>4. What is the unit of capacitance?<\/strong><\/p>\n<p><strong>Answer: <\/strong>The unit of capacitance is the <strong>farad (F)<\/strong>, where<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">1<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">1<\/span><\/span><\/span> farad =<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">1<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">1<\/span><\/span><\/span> coulomb per volt.<\/p>\n<p><strong>5. What is the energy stored in a capacitor?<\/strong><\/p>\n<p><strong>Answer: <\/strong>The energy stored in a capacitor is<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>U<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mi>C<\/mi><msup><mi>V<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">U = \\frac{1}{2} C V^2<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">U<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\">C<\/span><span class=\"mord\"><span class=\"mord mathnormal\">V<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, where<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>C<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">C<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><\/span><\/span> is capacitance and<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>V<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">V<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">V<\/span><\/span><\/span> is the potential difference.<\/p>\n<p><strong>6. What is the relation between electric field and electrostatic potential?<\/strong><\/p>\n<p><strong>Answer: <\/strong>The electric field<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>E<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">E<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">E<\/span><\/span><\/span> is the negative gradient of the electrostatic potential:<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>E<\/mi><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mrow><mi>d<\/mi><mi>V<\/mi><\/mrow><mrow><mi>d<\/mi><mi>r<\/mi><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">E = &#8211; \\frac{dV}{dr}<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">E<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">\u2212<\/span><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mord mathnormal mtight\">r<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><span class=\"mord mathnormal mtight\">V<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/p>\n<p><strong>7. What is the effect of a dielectric on capacitance?<\/strong><\/p>\n<p><strong>Answer: <\/strong>A dielectric increases the capacitance of a capacitor by a factor of the dielectric constant<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>k<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">k<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">k<\/span><\/span><\/span>, so<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>C<\/mi><mo lspace=\"0em\" mathvariant=\"normal\" rspace=\"0em\">\u2032<\/mo><\/msup><mo>=<\/mo><mi>k<\/mi><mi>C<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">C&#8217; = kC<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">k<\/span><span class=\"mord mathnormal\">C<\/span><\/span><\/span>.<\/p>\n<p><strong>8. What happens to the capacitance of capacitors in series?<\/strong><\/p>\n<p><strong>Answer: <\/strong>In series, the total capacitance<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>C<\/mi><mi>t<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">C_t<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">C<\/span><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 mathnormal mtight\">t<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span> is less than the capacitance of any individual capacitor:<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mfrac><mn>1<\/mn><msub><mi>C<\/mi><mi>t<\/mi><\/msub><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><msub><mi>C<\/mi><mn>1<\/mn><\/msub><\/mfrac><mo>+<\/mo><mfrac><mn>1<\/mn><msub><mi>C<\/mi><mn>2<\/mn><\/msub><\/mfrac><mo>+<\/mo><mo>\u2026<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{1}{C_t} = \\frac{1}{C_1} + \\frac{1}{C_2} + \\dots<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">C<\/span><span class=\"msupsub\"><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">C<\/span><span class=\"msupsub\"><span class=\"sizing reset-size3 size1 mtight\">1<\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">C<\/span><span class=\"msupsub\"><span class=\"sizing reset-size3 size1 mtight\">2<\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"minner\">\u2026<\/span><\/span><\/span><\/p>\n<p><strong>9. What happens to the capacitance of capacitors in parallel?<\/strong><\/p>\n<p><strong>Answer: <\/strong>In parallel, the total capacitance<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>C<\/mi><mi>t<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">C_t<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">C<\/span><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 mathnormal mtight\">t<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span> is the sum of the individual capacitances:<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>C<\/mi><mi>t<\/mi><\/msub><mo>=<\/mo><msub><mi>C<\/mi><mn>1<\/mn><\/msub><mo>+<\/mo><msub><mi>C<\/mi><mn>2<\/mn><\/msub><mo>+<\/mo><mo>\u2026<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">C_t = C_1 + C_2 + \\dots<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">C<\/span><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 mathnormal mtight\">t<\/span><\/span><\/span><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\">C<\/span><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\">1<\/span><\/span><\/span><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\">C<\/span><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\">2<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"minner\">\u2026<\/span><\/span><\/span><\/p>\n<p><strong>10. What is the dielectric constant?<\/strong><\/p>\n<p><strong>Answer: <\/strong>The dielectric constant<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>k<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">k<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">k<\/span><\/span><\/span> is a measure of a material&#8217;s ability to reduce the electric field between the plates of a capacitor.<\/p>\n<p><strong>11. What is the formula for the energy density of an electric field?<\/strong><\/p>\n<p><strong>Answer: <\/strong>The energy density<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>u<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">u<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">u<\/span><\/span><\/span> of an electric field is<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>u<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><msub><mi>\u03f5<\/mi><mn>0<\/mn><\/msub><msup><mi>E<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">u = \\frac{1}{2} \\epsilon_0 E^2<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">u<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03f5<\/span><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\">0<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, where<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>\u03f5<\/mi><mn>0<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">\\epsilon_0<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">\u03f5<\/span><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\">0<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span> is the permittivity of free space and<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>E<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">E<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">E<\/span><\/span><\/span> is the electric field.<\/p>\n<p><strong>12. What is the unit of electric potential?<\/strong><\/p>\n<p><strong>Answer: <\/strong>The unit of electric potential is the <strong>volt (V)<\/strong>, where<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">1<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">1<\/span><\/span><\/span> volt =<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">1<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">1<\/span><\/span><\/span> joule per coulomb.<\/p>\n<p><strong>13. What is the formula for total energy stored in a parallel combination of capacitors?<\/strong><\/p>\n<p><strong>Answer: <\/strong>The total energy stored in a parallel combination of capacitors is the sum of the energy stored in each capacitor:<\/p>\n<p>&nbsp;<\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>U<\/mi><mtext>total<\/mtext><\/msub><mo>=<\/mo><mo>\u2211<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><msub><mi>C<\/mi><mi>i<\/mi><\/msub><msup><mi>V<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">U_{\\text{total}} = \\sum \\frac{1}{2} C_i V^2<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">U<\/span><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\"><span class=\"mord text mtight\">total<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mop op-symbol large-op\">\u2211<\/span><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\">21<\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">C<\/span><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 mathnormal mtight\">i<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">V<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><strong>14. What is the effect of increasing the distance between plates in a parallel plate capacitor?<\/strong><\/p>\n<p><strong>Answer: <\/strong>Increasing the distance between plates decreases the capacitance, as<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>C<\/mi><mo>=<\/mo><mfrac><mrow><msub><mi>\u03f5<\/mi><mn>0<\/mn><\/msub><mi>A<\/mi><\/mrow><mi>d<\/mi><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">C = \\frac{\\epsilon_0 A}{d}<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">d<\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">\u03f5<\/span><span class=\"msupsub\"><span class=\"sizing reset-size3 size1 mtight\">0<\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"mord mathnormal mtight\">A<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>, where<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>d<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">d<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">d<\/span><\/span><\/span> is the distance.<\/p>\n<p><strong>15. What is the formula for the electric field between the plates of a parallel plate capacitor?<\/strong><\/p>\n<p><strong>Answer: <\/strong>The electric field between the plates of a parallel plate capacitor is<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>E<\/mi><mo>=<\/mo><mfrac><mi>\u03c3<\/mi><msub><mi>\u03f5<\/mi><mn>0<\/mn><\/msub><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">E = \\frac{\\sigma}{\\epsilon_0}<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">E<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">\u03f5<\/span><span class=\"msupsub\"><span class=\"sizing reset-size3 size1 mtight\">0<\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">\u03c3<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>, where<\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\u03c3<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\sigma<\/annotation><\/semantics><\/math>\n<p><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">\u03c3<\/span><\/span><\/span> is the surface charge density.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Important Questions with Answers for CBSE Class 12 Physics 1. What is electrostatic potential? 2. 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