When five capacitors with equal capacitances are connected in series, the equivalent capacitance of the combination is 6.99 mF. The capacitors are then reconnected so that a parallel combination of two capacitors is connected in series with a parallel combination of three capacitors. Determine the equivalent capacitance Cequiv of this combination in millifarads. Cequiv mF PC TOOLS X10<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n Let’s first address the scenario where five capacitors, each with the same capacitance ( C ), are connected in series. The formula for the equivalent capacitance of capacitors in series is:<\/p>\n\n\n\n [ Since the five capacitors have equal capacitances, the formula simplifies to:<\/p>\n\n\n\n [ Thus, the equivalent capacitance for five capacitors in series is:<\/p>\n\n\n\n [ We’re given that the equivalent capacitance for the five capacitors in series is 6.99 mF. Therefore:<\/p>\n\n\n\n [ Solving for ( C ), the capacitance of each individual capacitor:<\/p>\n\n\n\n [ Now, the capacitors are reconnected in a different configuration: two capacitors are connected in parallel, and this parallel combination is connected in series with another parallel combination of three capacitors.<\/p>\n\n\n\n The formula for capacitors in parallel is:<\/p>\n\n\n\n [ For two capacitors, the equivalent capacitance is:<\/p>\n\n\n\n [ For three capacitors, the equivalent capacitance is:<\/p>\n\n\n\n [ Finally, we need to find the equivalent capacitance of these two parallel combinations connected in series. The formula for two capacitors in series is:<\/p>\n\n\n\n [ Substituting ( C_1 = 69.9 \\, \\text{mF} ) and ( C_2 = 104.85 \\, \\text{mF} ):<\/p>\n\n\n\n [ Calculating the individual terms:<\/p>\n\n\n\n [ Thus:<\/p>\n\n\n\n [ Finally, the equivalent capacitance is:<\/p>\n\n\n\n [ The equivalent capacitance of the combination is approximately 42.02 mF<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" When five capacitors with equal capacitances are connected in series, the equivalent capacitance of the combination is 6.99 mF. The capacitors are then reconnected so that a parallel combination of two capacitors is connected in series with a parallel combination of three capacitors. Determine the equivalent capacitance Cequiv of this combination in millifarads. Cequiv mF […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-168473","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168473","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=168473"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168473\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=168473"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=168473"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=168473"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\\frac{1}{C_{\\text{equiv, series}}} = \\frac{1}{C_1} + \\frac{1}{C_2} + \\cdots + \\frac{1}{C_n}
]<\/p>\n\n\n\n
\\frac{1}{C_{\\text{equiv, series}}} = \\frac{5}{C}
]<\/p>\n\n\n\n
C_{\\text{equiv, series}} = \\frac{C}{5}
]<\/p>\n\n\n\n
\\frac{C}{5} = 6.99 \\, \\text{mF}
]<\/p>\n\n\n\n
C = 6.99 \\, \\text{mF} \\times 5 = 34.95 \\, \\text{mF}
]<\/p>\n\n\n\nStep 1: Equivalent Capacitance for Two Capacitors in Parallel<\/h3>\n\n\n\n
C_{\\text{equiv, parallel}} = C_1 + C_2 + \\cdots + C_n
]<\/p>\n\n\n\n
C_{\\text{parallel, 2}} = C + C = 2C = 2 \\times 34.95 \\, \\text{mF} = 69.9 \\, \\text{mF}
]<\/p>\n\n\n\nStep 2: Equivalent Capacitance for Three Capacitors in Parallel<\/h3>\n\n\n\n
C_{\\text{parallel, 3}} = C + C + C = 3C = 3 \\times 34.95 \\, \\text{mF} = 104.85 \\, \\text{mF}
]<\/p>\n\n\n\nStep 3: Equivalent Capacitance of Two Parallel Combinations in Series<\/h3>\n\n\n\n
\\frac{1}{C_{\\text{equiv, series}}} = \\frac{1}{C_1} + \\frac{1}{C_2}
]<\/p>\n\n\n\n
\\frac{1}{C_{\\text{equiv, series}}} = \\frac{1}{69.9} + \\frac{1}{104.85}
]<\/p>\n\n\n\n
\\frac{1}{69.9} \\approx 0.0143 \\quad \\text{and} \\quad \\frac{1}{104.85} \\approx 0.0095
]<\/p>\n\n\n\n
\\frac{1}{C_{\\text{equiv, series}}} = 0.0143 + 0.0095 = 0.0238
]<\/p>\n\n\n\n
C_{\\text{equiv, series}} = \\frac{1}{0.0238} \\approx 42.02 \\, \\text{mF}
]<\/p>\n\n\n\nFinal Answer:<\/h3>\n\n\n\n