{"id":3060,"date":"2018-06-05T17:38:50","date_gmt":"2018-06-06T00:38:50","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=3060"},"modified":"2018-06-05T17:38:50","modified_gmt":"2018-06-06T00:38:50","slug":"electric-charge-stored-in-capacitor-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/electric-charge-stored-in-capacitor-problems-and-solutions.htm","title":{"rendered":"Electric charge stored in capacitor \u2013 problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

1. <\/span><\/span>Determine the charge<\/a> in capacitor<\/a> <\/span><\/span>C<\/span><\/span>5<\/span><\/sub>.<\/span><\/span><\/p>\n

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

Capacitor <\/span><\/span>1 (C<\/span><\/span>1<\/span><\/sub>) = 6 F<\/span><\/span><\/p>\n

Capacitor<\/span><\/span> 2 (C<\/span><\/span>2<\/span><\/sub>) = 6 F<\/span><\/span><\/p>\n

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

Capacitor <\/span><\/span>4 (C<\/span><\/span>4<\/span><\/sub>) = 12 F<\/span><\/span><\/p>\n

Capacitor<\/span><\/span> 5 (C<\/span><\/span>5<\/span><\/sub>) = 6 F<\/span><\/span><\/p>\n

Voltage <\/span><\/span>(V) = 12 Volt<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> Charge in capacitor <\/span><\/span><\/a>(C<\/span><\/span>5<\/span><\/sub>)<\/span><\/span><\/p>\n

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

C<\/b><\/span><\/span>apa<\/b><\/span><\/span>c<\/b><\/span><\/span>itor<\/b><\/span><\/span><\/p>\n

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

1\/C<\/span><\/span>A<\/span><\/sub> = 1\/C<\/span><\/span>2<\/span><\/sub> + 1\/C<\/span><\/span>3 <\/span><\/sub>= 1\/6 + 1\/3 = 1\/6 + 2\/6 = 3\/6 <\/span><\/span><\/p>\n

C<\/span><\/span>A<\/span><\/sub> = 6\/3 = 2 Farad<\/span><\/span><\/p>\n

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

1\/C<\/span><\/span>B<\/span><\/sub> = 1\/C<\/span><\/span>4<\/span><\/sub> + 1\/C<\/span><\/span>5<\/span><\/sub> = 1\/12 + 1\/6 = 1\/12 + 2\/12 = 3\/12<\/span><\/span><\/p>\n

C<\/span><\/span>B<\/sub> <\/span><\/span>= 12\/3 = 4 Farad <\/span><\/span><\/p>\n

Capacitor <\/span><\/span>C<\/span><\/span>A<\/span><\/sub> and capacitor <\/span><\/span>C<\/span><\/span>B<\/span><\/sub> are connected <\/span><\/span>i<\/span><\/span>n parallel<\/span><\/span><\/a>. <\/span><\/span>The equivalent capacitor :<\/span><\/span><\/p>\n

C<\/span><\/span>C<\/span><\/sub> = C<\/span><\/span>A<\/span><\/sub> + C<\/span><\/span>B<\/span><\/sub> = 2 + 4 = 6 Farad<\/span><\/span><\/p>\n

Capacitor <\/span><\/span>C<\/span><\/span>1<\/span><\/sub> and capacitor <\/span><\/span>C<\/span><\/span>C <\/span><\/sub>are connected in series <\/span><\/span>:<\/span><\/span><\/p>\n

1\/C = 1\/C<\/span><\/span>1<\/span><\/sub> + 1\/C<\/span><\/span>C<\/span><\/sub> = 1\/6 F + 1\/6 F = 2\/6 <\/span><\/span><\/p>\n

C = 6\/2 = 3 Farad<\/span><\/span><\/p>\n

Electric charge<\/b><\/span><\/span><\/p>\n

Electric charge in capacitor <\/u><\/span><\/span>C :<\/u><\/span><\/span><\/p>\n

q = V C = (12 Volt)(3 Farad) = 36 Coulomb<\/span><\/span><\/p>\n

C<\/span><\/span>apa<\/span><\/span>c<\/span><\/span>itor 1 <\/span><\/span>and c<\/span><\/span>apa<\/span><\/span>c<\/span><\/span>itor C<\/span><\/span>C<\/span> <\/sub>are connected in series so that electric charge in capacitor <\/span><\/span>C = <\/span><\/span>electric charge in capacitor <\/span><\/span>C<\/span><\/span>1<\/span><\/sub> = <\/span><\/span>electric charge in capacitor <\/span><\/span>C<\/span><\/span>C<\/span><\/sub> = 36 Coulomb.<\/span><\/span><\/p>\n

Capacitance of c<\/span><\/span>apa<\/span><\/span>c<\/span><\/span>itor C<\/span><\/span>C<\/span><\/sub> is <\/span><\/span>6 Farad <\/span><\/span>and charge in capacitor C<\/span><\/span>C <\/span><\/sub>is <\/span><\/span>36 Coulomb. <\/span><\/span>The voltage of the capacitor <\/span><\/span>C<\/span><\/span>C <\/span><\/sub>is <\/span><\/span>:<\/span><\/span> V = q\/C<\/span><\/span>C<\/span><\/sub> = 36 Coulomb \/ 6 Farad = 6 Volt <\/span><\/span><\/p>\n

Capacitor <\/span><\/span>C<\/span><\/span>C<\/span> <\/sub>is the equivalent capacitor for capacitor <\/span><\/span>C<\/span><\/span>A<\/span><\/sub> and capacitor <\/span><\/span>C<\/span><\/span>B <\/span><\/sub>connected in parallel. Voltage of the capacitor <\/span><\/span>C<\/span><\/span>C<\/span><\/sub> (V<\/span><\/span>C<\/span><\/sub>) = <\/span><\/span>voltage in capacitor <\/span><\/span>C<\/span><\/span>A <\/span><\/sub>(V<\/span><\/span>A<\/span><\/sub>) = <\/span><\/span>voltage in capacitor <\/span><\/span>C<\/span><\/span>B<\/span><\/sub> (V<\/span><\/span>B<\/span><\/sub>) = 6 Volt.<\/span><\/span><\/p>\n

Electric charge in capacitor <\/u><\/span><\/span>C<\/u><\/span><\/span>B <\/u><\/span><\/sub>:<\/u><\/span><\/span><\/p>\n

q<\/span><\/span>B<\/span><\/sub> = V<\/span><\/span>B <\/span><\/sub>C<\/span><\/span>B <\/span><\/sub>= (6 Volt)(4 Farad) = 24 Coulomb<\/span><\/span><\/p>\n

Capacitor <\/span><\/span>C<\/span><\/span>B<\/span><\/sub> is the equivalent capacitor for capacitor <\/span><\/span>C<\/span><\/span>4<\/sub> <\/span><\/span>and <\/span><\/span>C<\/span><\/span>5<\/span> <\/sub>connected in series<\/span><\/span>. <\/span><\/span>Connected in series so that the electric charge in capacitor <\/span><\/span>C<\/span><\/span>B<\/span><\/sub> (q<\/span><\/span>B<\/span><\/sub>) = <\/span><\/span>the electric charge in capacitor <\/span><\/span>C<\/span><\/span>4<\/span><\/sub> (q<\/span><\/span>4<\/span><\/sub>) = <\/span><\/span>the electric charge in capacitor <\/span><\/span>C<\/span><\/span>5<\/span><\/sub> (q<\/span><\/span>5<\/span><\/sub>) = 24 Coulomb.<\/span><\/span><\/p>\n

2. Five identical <\/span>capacitors with a capacitance of 20 \u00b5F are connected in series and parallel, as shown in the figure below, with a source of voltage 6 volts. Determine total energy<\/a> stored in capacitor C5<\/sub>.<\/span><\/span><\/p>\n

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

Capacitor C1<\/sub> = C2<\/sub> = C3<\/sub> = C4<\/sub> = C5<\/sub> = 20 \u00b5F <\/span><\/span><\/p>\n

Voltage (V) = 6 Volt<\/span><\/span><\/p>\n

Wanted :<\/u> Electric charge stored in capacitor C5<\/sub><\/span><\/span><\/p>\n

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

Capacitor<\/b><\/span><\/span><\/p>\n

Capacitor <\/span><\/span>C<\/span><\/span>1<\/span><\/sub> and capacitor <\/span><\/span>C<\/span><\/span>2<\/span><\/sub> are connected in series. The equivalent capacitor :<\/span><\/span><\/p>\n

1\/C<\/span><\/span>A<\/span><\/sub> = 1\/C<\/span><\/span>1<\/span><\/sub> + 1\/C<\/span><\/span>2 <\/span><\/sub>= 1\/20 + 1\/20 = 2\/20 <\/span><\/span><\/p>\n

C<\/span><\/span>A<\/span><\/sub> = 20\/2 = 10 \u00b5F <\/span><\/span><\/p>\n

Capacitor <\/span><\/span>C<\/span><\/span>3<\/span><\/sub> and capacitor <\/span><\/span>C<\/span><\/span>4<\/span><\/sub> are connected in series<\/span><\/span>. <\/span><\/span>The equivalent capacitor :<\/span><\/span><\/p>\n

1\/C<\/span><\/span>B<\/span><\/sub> = 1\/C<\/span><\/span>3<\/span><\/sub> + 1\/C<\/span><\/span>4<\/span><\/sub> = 1\/20 + 1\/20 = 2\/20<\/span><\/span><\/p>\n

CB<\/sub> = 20\/2 = 10 \u00b5F <\/span><\/span><\/p>\n

Capacitor <\/span><\/span>C<\/span><\/span>A<\/span><\/sub> and capacitor <\/span><\/span>C<\/span><\/span>B<\/span><\/sub> are connected in parallel<\/span><\/span>. <\/span><\/span>The equivalent capacitor :<\/span><\/span><\/p>\n

C<\/span><\/span>C<\/span><\/sub> = C<\/span><\/span>A<\/span><\/sub> + C<\/span><\/span>B<\/span><\/sub> = 10 + 10 = 20 \u00b5F <\/span><\/span><\/p>\n

Capacitor <\/span><\/span>C<\/span><\/span>C<\/span><\/sub> and capacitor <\/span><\/span>C<\/span><\/span>5<\/span><\/sub> are connected in series :<\/span><\/span><\/p>\n

1\/C = 1\/C<\/span><\/span>C<\/span><\/sub> + 1\/C<\/span><\/span>5<\/span><\/sub> = 1\/20 + 1\/20 = 2\/20<\/span><\/span><\/p>\n

C = 20\/2 = 10 \u00b5F <\/span><\/span><\/p>\n

Electric charge<\/b><\/span><\/span><\/p>\n

Electric charge in the equivalent capacitor <\/span><\/span>C :<\/span><\/span><\/p>\n

\u00a0q = V C = (6 Volt)(10 x 10<\/span><\/span>-6 <\/span><\/span><\/sup>Farad) = 60 x 10<\/span><\/span>-6<\/span><\/span><\/sup> Coulomb = 60 \u00b5C <\/span><\/span><\/p>\n

Capacitor <\/span><\/span>C<\/span><\/span>C <\/span><\/sub>and capacitor <\/span><\/span>5 <\/span><\/span>are connected in series so that electric charge in the equivalent capacitor <\/span><\/span>C = <\/span><\/span>electric charge in capacitor <\/span><\/span>C<\/span><\/span>C <\/span><\/sub>= <\/span><\/span>electric charge in capacitor <\/span><\/span>C<\/span><\/span>5<\/span><\/span><\/sub> = 60 \u00b5C.<\/span><\/span><\/p>\n

3. <\/span><\/span>Five capacitors are connected in series and parallel as shown in figure below. Determine electric charges in capacitor <\/span><\/span>C<\/span><\/span>1<\/sub> <\/span><\/span>(1 <\/span><\/span>\u00b5 = 10<\/span><\/span>-6<\/span><\/span><\/sup>)<\/span><\/span><\/p>\n

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

Capacitor <\/span><\/span>1 (C<\/span><\/span>1<\/span><\/sub>) = <\/span><\/span>capacitor <\/span><\/span>5 (C<\/span><\/span>5<\/span><\/sub>) = 9 <\/span><\/span>\u00b5<\/span><\/span>F<\/span><\/span><\/p>\n

Capacitor <\/span><\/span>2 (C<\/span><\/span>2<\/span><\/sub>) = <\/span><\/span>capacitor <\/span><\/span>3 (C<\/span><\/span>3<\/span><\/sub>) = <\/span><\/span>capacitor <\/span><\/span>4 (C<\/span><\/span>4<\/span><\/sub>) = 6 <\/span><\/span>\u00b5<\/span><\/span>F <\/span><\/span><\/p>\n

Voltage <\/span><\/span>(V) = 12 Volt<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> Electric charge in capacitor <\/span><\/span>C<\/span><\/span>1<\/span><\/span><\/sub><\/p>\n

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

Capacitor<\/b><\/span><\/span><\/p>\n

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

1\/C<\/span><\/span>A<\/span><\/sub> = 1\/C<\/span><\/span>2<\/span><\/sub> + 1\/C<\/span><\/span>3 <\/span><\/sub>= 1\/6 + 1\/6 = 2\/6 <\/span><\/span><\/p>\n

C<\/span><\/span>A<\/span><\/sub> = 6\/2 = 3 <\/span><\/span>\u00b5<\/span><\/span>F<\/span><\/span><\/p>\n

Capacitor <\/span><\/span>C<\/span><\/span>A<\/span><\/sub> and capacitor <\/span><\/span>C<\/span><\/span>4<\/span> <\/sub>are connected in parallel<\/span><\/span>. <\/span><\/span>The equivalent capacitor :<\/span><\/span><\/p>\n

C<\/span><\/span>B<\/span><\/sub> = C<\/span><\/span>A<\/span><\/sub> + C<\/span><\/span>4<\/span><\/sub> = 3 + 6 = 9 <\/span><\/span>\u00b5<\/span><\/span>F <\/span><\/span><\/p>\n

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

1\/C = 1\/C<\/span><\/span>1<\/span><\/sub> + 1\/C<\/span><\/span>B<\/sub> <\/span><\/span>+ 1\/C<\/span><\/span>5<\/span><\/sub> = 1\/9 + 1\/9 + 1\/9 = 3\/9<\/span><\/span><\/p>\n

C = 9\/3 = 3 <\/span><\/span>\u00b5F = 3 x 10<\/span><\/span>-6 <\/span><\/span><\/sup>Farad<\/span><\/span><\/p>\n

Electric charge<\/b><\/span><\/span><\/p>\n

Electric charge in the equivalent capacitor <\/span><\/span>C :<\/span><\/span><\/p>\n

q = V C = (12 Volt)(3 x 10<\/span><\/span>-6 <\/span><\/span><\/sup>Farad) = 36 x 10<\/span><\/span>-6<\/span><\/span><\/sup> Coulomb = 36 \u00b5C <\/span><\/span><\/p>\n

Capacitor <\/span><\/span>C<\/span><\/span>1<\/span><\/sub>, <\/span><\/span>capacitor <\/span><\/span>C<\/span><\/span>B<\/span> <\/sub>and capacitor <\/span><\/span>C<\/span><\/span>5 <\/span><\/sub>are connected in series so that electric charge in the equivalent capacitor <\/span><\/span>C = <\/span><\/span>electric charge in capacitor <\/span><\/span>C<\/span><\/span>1 <\/span><\/sub>= <\/span><\/span>electric charge in the equivalent capacitor <\/span><\/span>C<\/span><\/span>B <\/span><\/sub>= <\/span><\/span>electric charge in capacitor <\/span><\/span>C<\/span><\/span>5<\/span><\/sub> = 36 \u00b5C<\/span><\/span>.<\/span><\/span><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"

1. Determine the charge in capacitor C5. Known : Capacitor 1 (C1) = 6 F Capacitor 2 (C2) = 6 F Capacitor 3 (C3) = 3 F Capacitor 4 (C4) = 12 F Capacitor 5 (C5) = 6 F Voltage (V) = 12 Volt<\/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":"Electric charge stored in capacitor \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-3060","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\/3060","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=3060"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/3060\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=3060"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=3060"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=3060"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}