{"id":246859,"date":"2022-09-10T09:12:02","date_gmt":"2022-09-10T03:42:02","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/a-parallel-plate-capacitor-having-cross-sectional-area-a-and-separation-d-has-air-in-between-the-plates-now-an-insulating-slab-of-same-area-but-thickness-d-2-is-inserted-between-the-plates-as-shown\/"},"modified":"2025-06-26T18:17:47","modified_gmt":"2025-06-26T12:47:47","slug":"a-parallel-plate-capacitor-having-cross-sectional-area-a-and-separation-d-has-air-in-between-the-plates-now-an-insulating-slab-of-same-area-but-thickness-d-2-is-inserted-between-the-plates-as-shown","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-parallel-plate-capacitor-having-cross-sectional-area-a-and\/","title":{"rendered":"A parallel plate capacitor having cross-sectional area A and separation d has air in between the plates.Now, an insulating slab of same area but thickness d \/ 2 is inserted between the plates as shown infigure having dielectric constant K(= 4). The ratio of new capacitance to its original capacitance will be\u00a0\u00a0"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"A parallel plate capacitor having cross-sectional area A","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"A parallel plate capacitor having cross-sectional area A and separation d has air in between the plates.Now, an insulating slab of same area but thickness d \/ 2 is inserted between the plates as shown infigure having dielectric constant K(= 4). The ratio of new capacitance to its original capacitance will be\u00a0\u00a0","custom_permalink":"question\/physics\/a-parallel-plate-capacitor-having-cross-sectional-area-a-and\/"},"categories":[],"acf":{"question":"<p>A parallel plate capacitor having cross-sectional area A and separation d has air in between the plates.<br>Now, an insulating slab of same area but thickness d \/ 2 is inserted between the plates as shown in<br>figure having dielectric constant K(= 4). The ratio of new capacitance to its original capacitance will be<br>&nbsp;<\/p><p>&nbsp;<\/p>","options":[{"option":"<p>2 : 1<\/p>","correct":false},{"option":"<p>8 : 5<\/p>","correct":true},{"option":"<p>6 : 5<\/p>","correct":false},{"option":"<p>4 : 1<\/p>","correct":false}],"solution":"<p>Capacitance of parallel plate capacitor when medium is air<\/p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi mathvariant=\"normal\">C<\/mi><mn>0<\/mn><\/msub><mo>=<\/mo><mfrac><mrow><msub><mi mathvariant=\"normal\">\u03b5<\/mi><mn>0<\/mn><\/msub><mi mathvariant=\"normal\">A<\/mi><\/mrow><mi mathvariant=\"normal\">d<\/mi><\/mfrac><\/math>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;\u2026 (i)<\/p><p>According to second condition,<\/p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; A' = A, t = d \/ 2, K = 4<\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><\/math>&nbsp;Capacitance,&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi mathvariant=\"normal\">C<\/mi><mo>=<\/mo><mfrac><mrow><msub><mi mathvariant=\"normal\">\u03b5<\/mi><mn>0<\/mn><\/msub><mi mathvariant=\"normal\">A<\/mi><\/mrow><mrow><mo>(<\/mo><mi mathvariant=\"normal\">d<\/mi><mo>-<\/mo><mi mathvariant=\"normal\">t<\/mi><mo>)<\/mo><mo>&nbsp;<\/mo><mo>+<\/mo><mo>&nbsp;<\/mo><mstyle displaystyle=\"true\"><mfrac><mi mathvariant=\"normal\">t<\/mi><mi mathvariant=\"normal\">K<\/mi><\/mfrac><\/mstyle><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><msub><mi mathvariant=\"normal\">\u03b5<\/mi><mn>0<\/mn><\/msub><mi mathvariant=\"normal\">A<\/mi><\/mrow><mrow><mfenced><mrow><mi mathvariant=\"normal\">d<\/mi><mo>-<\/mo><mstyle displaystyle=\"true\"><mfrac><mi mathvariant=\"normal\">d<\/mi><mn>2<\/mn><\/mfrac><\/mstyle><\/mrow><\/mfenced><mo>+<\/mo><mstyle displaystyle=\"true\"><mfrac><mrow><mi mathvariant=\"normal\">d<\/mi><mo>\/<\/mo><mn>2<\/mn><\/mrow><mn>4<\/mn><\/mfrac><\/mstyle><\/mrow><\/mfrac><\/math><\/p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mfrac><mrow><msub><mi mathvariant=\"normal\">\u03b5<\/mi><mn>0<\/mn><\/msub><mi mathvariant=\"normal\">A<\/mi><\/mrow><mrow><mstyle displaystyle=\"true\"><mfrac><mi mathvariant=\"normal\">d<\/mi><mn>2<\/mn><\/mfrac><\/mstyle><mo>+<\/mo><mstyle displaystyle=\"true\"><mfrac><mi mathvariant=\"normal\">d<\/mi><mn>8<\/mn><\/mfrac><\/mstyle><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mn>8<\/mn><mn>5<\/mn><\/mfrac><mo>\u00b7<\/mo><mfrac><mrow><msub><mi mathvariant=\"normal\">\u03b5<\/mi><mn>0<\/mn><\/msub><mi mathvariant=\"normal\">A<\/mi><\/mrow><mi mathvariant=\"normal\">d<\/mi><\/mfrac><\/math><\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><\/math>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mi mathvariant=\"normal\">C<\/mi><msub><mi mathvariant=\"normal\">C<\/mi><mn>0<\/mn><\/msub><\/mfrac><mo>=<\/mo><mfrac><mrow><mstyle displaystyle=\"true\"><mfrac><mn>8<\/mn><mn>5<\/mn><\/mfrac><\/mstyle><mo>\u00b7<\/mo><mstyle displaystyle=\"true\"><mfrac><mrow><msub><mi mathvariant=\"normal\">\u03b5<\/mi><mn>0<\/mn><\/msub><mi mathvariant=\"normal\">A<\/mi><\/mrow><mi mathvariant=\"normal\">d<\/mi><\/mfrac><\/mstyle><\/mrow><mstyle displaystyle=\"true\"><mfrac><mrow><msub><mi mathvariant=\"normal\">\u03b5<\/mi><mn>0<\/mn><\/msub><mi mathvariant=\"normal\">A<\/mi><\/mrow><mi mathvariant=\"normal\">d<\/mi><\/mfrac><\/mstyle><\/mfrac><\/math><\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u21d2<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mfrac><mi mathvariant=\"normal\">C<\/mi><msub><mi mathvariant=\"normal\">C<\/mi><mn>0<\/mn><\/msub><\/mfrac><mo>=<\/mo><mfrac><mn>8<\/mn><mn>5<\/mn><\/mfrac><\/math><\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u21d2<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mo>&nbsp;<\/mo><mi mathvariant=\"normal\">C<\/mi><mo>&nbsp;<\/mo><mo>:<\/mo><mo>&nbsp;<\/mo><msub><mi mathvariant=\"normal\">C<\/mi><mn>0<\/mn><\/msub><mo>=<\/mo><mn>8<\/mn><mo>&nbsp;<\/mo><mo>:<\/mo><mo>&nbsp;<\/mo><mn>5<\/mn><\/math><\/p>","subject":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>A parallel plate capacitor having cross-sectional area A and separation d has air in between the plates.Now, an insulating slab of same area but thickness d \/ 2 is inserted between the plates as shown infigure having dielectric constant K(= 4). 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