{"id":1401,"date":"2018-03-07T05:58:44","date_gmt":"2018-03-06T21:58:44","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=1401"},"modified":"2018-03-07T05:58:44","modified_gmt":"2018-03-06T21:58:44","slug":"capacitors-in-series-and-parallel-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/capacitors-in-series-and-parallel-problems-and-solutions.htm","title":{"rendered":"Capacitors in series and parallel \u2013 problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

1. Three capacitors, C<\/span><\/span>1<\/span><\/sub> = 2 \u03bcF, C<\/span><\/span>2<\/span><\/sub> = 4 \u03bcF, C<\/span><\/span>3<\/span><\/sub> = 4 \u03bcF, are connected in series and parallel<\/a>. Determine the capacitance of a single capacitor that will have the same effect as the combination.<\/span><\/span><\/p>\n

\"CapacitorsKnown :<\/u><\/span><\/span><\/p>\n

Capacitor<\/a> C<\/span><\/span>1<\/span><\/sub> = 2<\/span><\/span> \u03bc<\/span><\/span>F<\/span><\/span><\/p>\n

Capacitor C<\/span><\/span>2<\/span><\/sub> = 4<\/span><\/span> \u03bc<\/span><\/span>F<\/span><\/span><\/p>\n

Capacitor C<\/span><\/span>3<\/span><\/sub> = 4<\/span><\/span> \u03bc<\/span><\/span>F<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> The equivalent capacitance (C)<\/span><\/span><\/p>\n

Solution :<\/u><\/span><\/span><\/p>\n

Capacitor <\/span><\/span>C<\/span><\/span>2<\/span><\/sub> and C<\/span><\/span>3<\/span><\/sub> connected in parallel. The equivalent capacitance : <\/span><\/span><\/p>\n

C<\/span><\/span>P <\/span><\/sub>= C<\/span><\/span>2<\/span><\/sub> + C<\/span><\/span>3 <\/span><\/sub>= 4 + 4 = 8 <\/span><\/span>\u03bc<\/span><\/span>F<\/span><\/span><\/p>\n

Capacitor <\/span><\/span>C<\/span><\/span>1<\/span><\/sub> and C<\/span><\/span>p <\/span><\/sub>connected in series. The equivalent capacitance : <\/span><\/span><\/p>\n

1\/C = 1\/C<\/span><\/span>1<\/span><\/sub> + 1\/<\/span><\/span>C<\/span><\/span>P <\/span><\/sub> = 1\/2 + 1\/<\/span><\/span>8 = 4<\/span><\/span>\/<\/span><\/span>8 + 1\/8 = 5\/8 <\/span><\/span><\/p>\n

C = 8\/5 <\/span><\/span>\u03bc<\/span><\/span>F <\/span><\/span><\/p>\n

<\/p>\n

2. Five <\/span><\/span>capacitors, C<\/span><\/span>1<\/span><\/sub> = 2 \u03bcF, C<\/span><\/span>2<\/span><\/sub> = 4 \u03bcF, C<\/span><\/span>3<\/span><\/sub> = 6 \u03bcF, C<\/span><\/span>4<\/span><\/sub> = 5 \u03bcF, C<\/span><\/span>5<\/span><\/sub> = 10 \u03bcF, are connected in series and parallel. Determine the capacitance of a single capacitor that will have the same effect as the combination.<\/span><\/span><\/p>\n

Known :<\/u><\/span><\/span><\/p>\n

\"CapacitorsCapacitor C<\/span><\/span>1<\/span><\/sub> = 2<\/span><\/span> \u03bc<\/span><\/span>F<\/span><\/span><\/p>\n

Capacitor C<\/span><\/span>2<\/span><\/sub> = 4 <\/span><\/span>\u03bc<\/span><\/span>F<\/span><\/span><\/p>\n

Capacitor C<\/span><\/span>3<\/span><\/sub> = 6 <\/span><\/span>\u03bc<\/span><\/span>F<\/span><\/span><\/p>\n

Capacitor C<\/span><\/span>4<\/span><\/sub> = 5 <\/span><\/span>\u03bc<\/span><\/span>F<\/span><\/span><\/p>\n

Capacitor C<\/span><\/span>5<\/span><\/sub> = 10 <\/span><\/span>\u03bc<\/span><\/span>F<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> The equivalent capacitance <\/span><\/span>(C)<\/span><\/span><\/p>\n

Solution :<\/u><\/span><\/span><\/p>\n

Capacitor <\/span><\/span>C<\/span><\/span>2<\/span><\/sub> and C<\/span><\/span>3<\/span><\/sub> are connected in parallel. The equivalent capacitance :<\/span><\/span><\/p>\n

C<\/span><\/span>P <\/span><\/sub>= C<\/span><\/span>2<\/span><\/sub> + C<\/span><\/span>3 <\/span><\/sub><\/p>\n

C<\/span><\/span>P<\/span><\/sub> = 4 + 6 <\/span><\/span><\/p>\n

C<\/span><\/span>P <\/span><\/sub>= 10 <\/span><\/span>\u03bc<\/span><\/span>F<\/span><\/span><\/p>\n

Capacitor <\/span><\/span>C<\/span><\/span>1<\/span><\/sub>, C<\/span><\/span>P<\/span><\/sub>, C<\/span><\/span>4<\/span><\/sub> and C<\/span><\/span>5<\/span><\/sub> are connected in series. The equivalent capacitance :<\/span><\/span><\/p>\n

1\/C = 1\/C<\/span><\/span>1<\/span><\/sub> + 1\/<\/span><\/span>C<\/span><\/span>P <\/span><\/sub>+ <\/span><\/span>1\/<\/span><\/span>C<\/span><\/span>4 <\/span><\/sub>+ <\/span><\/span>1\/<\/span><\/span>C<\/span><\/span>5<\/sub> <\/span><\/span><\/p>\n

1\/C = 1\/2 + 1\/10 <\/span><\/span>+ <\/span><\/span>1\/<\/span><\/span>5 <\/span><\/span> + <\/span><\/span>1\/<\/span><\/span>10<\/span><\/span><\/p>\n

1\/C = 5\/10 + 1\/10 + 2\/10<\/span><\/span> + 1\/10<\/span><\/span><\/p>\n

1\/C = 9\/10 <\/span><\/span><\/p>\n

C = 10\/9 <\/span><\/span>\u03bc<\/span><\/span>F<\/span><\/span><\/p>\n

<\/p>\n

3. C<\/span><\/span>1 <\/span><\/sub>= 3 <\/span><\/span>\u03bc<\/span><\/span>F<\/span><\/span>, C<\/span><\/span>2<\/span><\/sub> = 4 <\/span><\/span>\u03bc<\/span><\/span>F and <\/span><\/span>C<\/span><\/span>3 <\/span><\/sub>= 3 <\/span><\/span>\u03bc<\/span><\/span>F, are connected in series and parallel. Determine the electric energy<\/a> on the circuits<\/a>. <\/span><\/span><\/p>\n

Known :<\/u><\/span><\/span><\/p>\n

Capacitor C<\/span><\/span>1<\/span><\/sub> = <\/span><\/span>3 <\/span><\/span>\u03bc<\/span><\/span>F\"Capacitors<\/span><\/span><\/p>\n

Capacitor C<\/span><\/span>2<\/span><\/sub> = 4 <\/span><\/span>\u03bc<\/span><\/span>F<\/span><\/span><\/p>\n

Capacitor C<\/span><\/span>3<\/span><\/sub> = <\/span><\/span>3 <\/span><\/span>\u03bc<\/span><\/span>F<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> The equivalent capacitance <\/span><\/span>(C)<\/span><\/span><\/p>\n

Solution :<\/u><\/span><\/span><\/p>\n

Capacitor <\/span><\/span>C<\/span><\/span>2<\/span><\/sub> and C<\/span><\/span>3<\/span><\/sub> are connected in parallel. The equivalent capacitance : <\/span><\/span><\/p>\n

C<\/span><\/span>P <\/span><\/sub>= C<\/span><\/span>2<\/span><\/sub> + C<\/span><\/span>3<\/sub> <\/span><\/span><\/p>\n

C<\/span><\/span>P<\/span><\/sub> = 4 + <\/span><\/span>3<\/span><\/span><\/p>\n

C<\/span><\/span>P <\/span><\/sub>= 7 <\/span><\/span>\u03bc<\/span><\/span>F<\/span><\/span><\/p>\n

Capacitor <\/span><\/span>C<\/span><\/span>1 <\/span><\/sub>and<\/span><\/span> C<\/span><\/span>P <\/span><\/sub>are connected in series. The equivalent capacitance : <\/span><\/span><\/p>\n

1\/C = 1\/C<\/span><\/span>1<\/span><\/sub> + 1\/<\/span><\/span>C<\/span><\/span>P<\/sub> <\/span><\/span><\/p>\n

1\/C = 1\/3 + 1\/7 <\/span><\/span><\/p>\n

1\/C = 7<\/span><\/span>\/21 + 3\/21<\/span><\/span><\/p>\n

1\/C = 10\/<\/span><\/span>21<\/span><\/span><\/p>\n

C = 21\/10<\/span><\/span><\/p>\n

C = 2.1 <\/span><\/span>\u03bc<\/span><\/span>F <\/span><\/span><\/p>\n

C = 2.1 x 10<\/span><\/span>-6<\/span><\/span><\/sup> F<\/span><\/span><\/p>\n

The electric energy on the circuits :<\/u><\/span><\/span><\/p>\n

E = \u00bd C V<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

E = \u00bd (<\/span><\/span>2.1 x 10<\/span><\/span>-6<\/span><\/span><\/sup>)(12<\/span><\/span>2<\/span><\/span><\/sup>) <\/span><\/span><\/p>\n

E = \u00bd (2.1 x 10<\/span><\/span>-6<\/span><\/span><\/sup>)(144) <\/span><\/span><\/p>\n

E = (2.1 x 10<\/span><\/span>-6<\/span><\/span><\/sup>)(72) <\/span><\/span><\/p>\n

E = 151.2 x 10<\/span><\/span>-6<\/span><\/span><\/sup> Joule <\/span><\/span><\/p>\n

E = 1.5 x 10<\/span><\/span>-4<\/span><\/span><\/sup> Joule <\/span><\/span><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"

1. Three capacitors, C1 = 2 \u03bcF, C2 = 4 \u03bcF, C3 = 4 \u03bcF, are connected in series and parallel. Determine the capacitance of a single capacitor that will have the same effect as the combination. Known : Capacitor C1 = 2 \u03bcF Capacitor C2 = 4 \u03bcF Capacitor C3 = 4 \u03bcF Wanted … Read more<\/a><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_seopress_titles_title":"","_seopress_titles_desc":"","_seopress_robots_index":"","_seopress_robots_follow":"","_seopress_robots_imageindex":"","_seopress_robots_snippet":"","_seopress_robots_primary_cat":"","_seopress_robots_breadcrumbs":"","_seopress_robots_freeze_modified_date":"","_seopress_robots_custom_modified_date":"","_seopress_robots_canonical":"","_seopress_social_fb_title":"","_seopress_social_fb_desc":"","_seopress_social_fb_img":"","_seopress_social_fb_img_attachment_id":0,"_seopress_social_fb_img_width":0,"_seopress_social_fb_img_height":0,"_seopress_social_twitter_title":"","_seopress_social_twitter_desc":"","_seopress_social_twitter_img":"","_seopress_social_twitter_img_attachment_id":0,"_seopress_social_twitter_img_width":0,"_seopress_social_twitter_img_height":0,"_seopress_redirections_value":"","_seopress_redirections_enabled":"","_seopress_redirections_enabled_regex":"","_seopress_redirections_logged_status":"","_seopress_redirections_param":"","_seopress_redirections_type":0,"_seopress_analysis_target_kw":"Capacitors in series and parallel \u2013 problems and solutions","_seopress_news_disabled":"","_seopress_video_disabled":"","_seopress_video":[],"_seopress_pro_schemas_manual":[],"_seopress_pro_rich_snippets_disable_all":"","_seopress_pro_rich_snippets_disable":[],"_seopress_pro_schemas":[],"footnotes":""},"categories":[3],"tags":[],"class_list":["post-1401","post","type-post","status-publish","format-standard","hentry","category-solved-problems-in-basic-physics"],"gt_translate_keys":[{"key":"link","format":"url"}],"_links":{"self":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/1401","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/comments?post=1401"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/1401\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=1401"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=1401"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=1401"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}