{"id":1395,"date":"2018-03-07T05:11:09","date_gmt":"2018-03-06T21:11:09","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=1395"},"modified":"2018-03-07T05:11:09","modified_gmt":"2018-03-06T21:11:09","slug":"capacitors-in-parallel-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/capacitors-in-parallel-problems-and-solutions.htm","title":{"rendered":"Capacitors in parallel \u2013 problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

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

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

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

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

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

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

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

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

The equivalent capacitance :<\/span><\/span><\/p>\n

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

C<\/span><\/span> = 4 <\/span><\/span>\u03bc<\/span><\/span>F + 2 <\/span><\/span>\u03bc<\/span><\/span>F + 3<\/span><\/span> \u03bc<\/span><\/span>F = 9 <\/span><\/span>\u03bc<\/span><\/span>F <\/span><\/span><\/p>\n

The equivalent capacitance of the entire combination is 9 <\/span><\/span>\u03bc<\/span><\/span>F. <\/span><\/span><\/p>\n

<\/p>\n

2. <\/span><\/span>Determine the charge<\/a> on capacitor <\/span><\/span>C<\/span><\/span>2 <\/span><\/sub>if the potential difference<\/a> between point A and B is <\/span><\/span>9 Volt…<\/span><\/span><\/p>\n

\"Capacitors<\/p>\n

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

C<\/span><\/span>apa<\/span><\/span>c<\/span><\/span>itor C<\/span><\/span>1<\/span><\/sub> = 20<\/span><\/span> \u03bc<\/span><\/span>F = 20 x 10<\/span><\/span>-6<\/span><\/span><\/sup> F<\/span><\/span><\/p>\n

C<\/span><\/span>apa<\/span><\/span>c<\/span><\/span>itor C<\/span><\/span>2<\/span><\/sub> = 30<\/span><\/span> \u03bc<\/span><\/span>F = 30 x 10<\/span><\/span>-6<\/span><\/span><\/sup> F<\/span><\/span><\/p>\n

Potential difference between point <\/span><\/span>A <\/span><\/span>and<\/span><\/span> B (V<\/span><\/span>AB<\/span><\/sub>) = 9 Volt<\/span><\/span><\/p>\n

Wanted <\/u><\/span><\/span>:<\/u><\/span><\/span> the charge on capacitor <\/span><\/span>C<\/span><\/span>2 <\/span><\/sub>(Q<\/span><\/span>2<\/span><\/sub>) <\/span><\/span><\/p>\n

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

Potential difference :<\/span><\/span><\/b><\/p>\n

Capacitors are connected in parallel<\/a> so that the potential difference between A and B (V<\/span><\/span>AB<\/span><\/sub>) = the potential difference on capacitor C<\/span><\/span>1 <\/span><\/sub>(V<\/span><\/span>1<\/span><\/sub>) = the potential difference on capacitor C<\/span><\/span>2<\/span><\/sub> (V<\/span><\/span>2<\/span><\/sub>) = 9 Volt. <\/span><\/span><\/p>\n

Electric charge on capacitor <\/u><\/span><\/span>C<\/u><\/span><\/span>2<\/u><\/span><\/sub> :<\/span><\/span><\/p>\n

Q<\/span><\/span>2<\/span><\/sub> = C<\/span><\/span>2<\/span><\/sub> V<\/span><\/span>2 <\/span><\/sub>= (30 x 10<\/span><\/span>-6<\/span><\/span><\/sup>)(9) = 270 x 10<\/span><\/span>-6<\/span><\/span><\/sup> C <\/span><\/span><\/p>\n

Q<\/span><\/span>2<\/span><\/sub> = 270 <\/span><\/span>\u03bc<\/span><\/span>C <\/span><\/span><\/p>\n

The electric charge on capacitor <\/span><\/span>C<\/span><\/span>2<\/span><\/sub> is <\/span><\/span> 27<\/span><\/span>0 <\/span><\/span>\u03bc<\/span><\/span>C.<\/span><\/span><\/p>\n

<\/p>\n

3. <\/span><\/span>Three <\/span><\/span>capacitors, C<\/span><\/span>1<\/span><\/sub> = 4 \u03bcF, C<\/span><\/span>2<\/span><\/sub> = 2 \u03bcF, C<\/span><\/span>3<\/span><\/sub> = 3 \u03bcF, are connected in parallel. The capacitor are charged. The potential difference on capacitor <\/span><\/span>C<\/span><\/span>2<\/span><\/sub> is 4 Volt. Determine<\/span><\/span><\/p>\n

(a) Electric charge on capacitor C<\/span><\/span>1<\/span><\/sub>, C<\/span><\/span>2<\/span><\/sub> and C<\/span><\/span>3<\/span><\/sub><\/p>\n

(b) Electric charge on the equivalent capacitor of the entire combination<\/span><\/span><\/p>\n

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

C<\/span><\/span>apa<\/span><\/span>c<\/span><\/span>itor C<\/span><\/span>1<\/span><\/sub> = 4 <\/span><\/span>\u03bc<\/span><\/span>F = 4 x 10<\/span><\/span>-6<\/span><\/span><\/sup> F<\/span><\/span><\/p>\n

C<\/span><\/span>apacitor C<\/span><\/span>2<\/span><\/sub> = 2 <\/span><\/span>\u03bc<\/span><\/span>F = 2 x 10<\/span><\/span>-6<\/span><\/span><\/sup> F<\/span><\/span><\/p>\n

C<\/span><\/span>apacitor C<\/span><\/span>3<\/span><\/sub> = 3 <\/span><\/span>\u03bc<\/span><\/span>F = 3 x 10<\/span><\/span>-6<\/span><\/span><\/sup> F<\/span><\/span><\/p>\n

Potential difference on capacitor <\/span><\/span>C<\/span><\/span>2<\/span><\/sub> (V<\/span><\/span>2<\/span><\/sub>) = 4 Volt<\/span><\/span><\/p>\n

Wanted <\/u><\/span><\/span>:<\/u><\/span><\/span> Electric charge on capacitor <\/span><\/span>C<\/span><\/span>3 <\/span><\/sub>(Q<\/span><\/span>3<\/span><\/sub>)<\/span><\/span><\/p>\n

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

(a) <\/b><\/span><\/span>Electric charge on capacitor <\/b><\/span><\/span>C<\/b><\/span><\/span>3<\/b><\/span><\/sub> <\/b><\/p>\n

The potential difference on capacitor <\/u><\/span><\/span>C<\/u><\/span><\/span>3<\/u><\/span><\/sub> :<\/span><\/span><\/p>\n

Capacitors are connected in parallel so that the potential difference on capacitor <\/span><\/span>C<\/span><\/span>3<\/span><\/sub> (V<\/span><\/span>3<\/span><\/sub>) = <\/span><\/span>the potential difference on capacitor <\/span><\/span>C<\/span><\/span>2<\/span><\/sub> (V<\/span><\/span>2<\/span><\/sub>) = <\/span><\/span>the potential difference on capacitor <\/span><\/span>C<\/span><\/span>1<\/span><\/sub> (V<\/span><\/span>1<\/span><\/sub>) = <\/span><\/span>the potential difference on equivalent capacitor <\/span><\/span>(V) = 4 Volt <\/span><\/span><\/p>\n

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

Q<\/span><\/span>1<\/span><\/sub> = C<\/span><\/span>1<\/span><\/sub> V<\/span><\/span>1 <\/span><\/sub>= (4 x 10<\/span><\/span>-6<\/span><\/span><\/sup>)(4) = 16 x 10<\/span><\/span>-6 <\/span><\/span><\/sup>C<\/span><\/span><\/p>\n

Q<\/span><\/span>1<\/span><\/sub> = 16 <\/span><\/span>\u03bc<\/span><\/span>C<\/span><\/span><\/p>\n

Electric charge on capacitor <\/u><\/span><\/span>C<\/u><\/span><\/span>2<\/u><\/span><\/sub> :<\/span><\/span><\/p>\n

Q<\/span><\/span>2<\/span><\/sub> = C<\/span><\/span>2<\/span><\/sub> V<\/span><\/span>2 <\/span><\/sub>= (2 x 10<\/span><\/span>-6<\/span><\/span><\/sup>)(4) = 8 x 10<\/span><\/span>-6 <\/span><\/span><\/sup>C<\/span><\/span><\/p>\n

Q<\/span><\/span>2<\/span><\/sub> = 8 <\/span><\/span>\u03bc<\/span><\/span>C<\/span><\/span><\/p>\n

Electric charge on capacitor <\/u><\/span><\/span>C<\/u><\/span><\/span>3<\/u><\/span><\/sub> :<\/span><\/span><\/p>\n

Q<\/span><\/span>3<\/span><\/sub> = C<\/span><\/span>3<\/span><\/sub> V<\/span><\/span>3 <\/span><\/sub>= (3 x 10<\/span><\/span>-6<\/span><\/span><\/sup>)(4) = 12 x 10<\/span><\/span>-6 <\/span><\/span><\/sup>C<\/span><\/span><\/p>\n

Q<\/span><\/span>3<\/span><\/sub> = 12 <\/span><\/span>\u03bc<\/span><\/span>C <\/span><\/span><\/p>\n

(b) <\/b><\/span><\/span>Electric charge on equivalent capacitor<\/b><\/span><\/span><\/p>\n

Q = Q<\/span><\/span>1<\/span><\/sub> + Q<\/span><\/span>2<\/span><\/sub> + Q<\/span><\/span>3<\/span><\/sub><\/p>\n

Q = 16 <\/span><\/span>\u03bc<\/span><\/span>C + 8 <\/span><\/span>\u03bc<\/span><\/span>C + 12 <\/span><\/span>\u03bc<\/span><\/span>C = 36 <\/span><\/span>\u03bc<\/span><\/span>C<\/span><\/span><\/p>\n

Alternative solution :<\/span><\/span><\/p>\n

The equivalent capacitance :<\/u><\/span><\/span><\/p>\n

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

C = 4 <\/span><\/span>\u03bc<\/span><\/span>F + 2 <\/span><\/span>\u03bc<\/span><\/span>F + 3 <\/span><\/span>\u03bc<\/span><\/span>F = 9 <\/span><\/span>\u03bc<\/span><\/span>F <\/span><\/span><\/p>\n

C = 9 x 10<\/span><\/span>-6<\/span><\/span><\/sup> F<\/span><\/span><\/p>\n

The potential difference on the equivalent capacitor :<\/u><\/span><\/span><\/p>\n

V<\/span><\/span>1<\/span><\/sub> = V<\/span><\/span>2<\/span><\/sub> = V<\/span><\/span>3<\/span><\/sub> = V = 4 Volt <\/span><\/span><\/p>\n

The electric charge on the equivalent capacitor :<\/u><\/span><\/span><\/p>\n

Q = C V = (9 x 10<\/span><\/span>-6<\/span><\/span><\/sup>)(4) = 36 x 10<\/span><\/span>-6 <\/span><\/span><\/sup>C<\/span><\/span><\/p>\n

Q = 36 <\/span><\/span>\u03bc<\/span><\/span>C <\/span><\/span><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"

1. Four capacitors, C1 = 2 \u03bcF, C2 = 1 \u03bcF, C3 = 3 \u03bcF, C4 = 4 \u03bcF, are connected in parallel. Determine the capacitance of a single capacitor that will have the same effect as the combination. Known : Capacitor C1 = 2 \u03bcF Capacitor C2 = 1 \u03bcF Capacitor C3 = 3 … 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 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-1395","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\/1395","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=1395"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/1395\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=1395"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=1395"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=1395"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}