{"id":1398,"date":"2018-03-07T05:33:37","date_gmt":"2018-03-06T21:33:37","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=1398"},"modified":"2018-03-07T05:33:37","modified_gmt":"2018-03-06T21:33:37","slug":"capacitors-in-series-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/capacitors-in-series-problems-and-solutions.htm","title":{"rendered":"Capacitors in series \u2013 problems and solutions"},"content":{"rendered":"

1. Four capacitors, 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 <\/span><\/span>series<\/span><\/span>. Determine the capacitance of a single capacitor<\/a> that will have the same effect as the combination.<\/span><\/span><\/p>\n

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

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

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

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

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

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

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

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

1\/C<\/span><\/span> = 6\/12 + 12\/12 + 4\/12<\/span><\/span> + 3\/12<\/span><\/span><\/p>\n

1\/C<\/span><\/span> = 25\/12<\/span><\/span><\/p>\n

C<\/span><\/span> = 12\/25 <\/span><\/span><\/p>\n

C<\/span><\/span> = 0.48 <\/span><\/span><\/p>\n

The equivalent capacitance of the entire combination <\/span><\/span>is <\/span><\/span>0.48 <\/span><\/span>\u03bc<\/span><\/span>F.<\/span><\/span><\/p>\n

<\/p>\n

2. Determine the charge on capacitor C<\/span><\/span>1<\/span><\/sub> if the potential difference<\/a> between <\/span><\/span>P<\/span><\/span> and <\/span><\/span>Q<\/span><\/span> is <\/span><\/span>12 <\/span><\/span>Volt…<\/span><\/span><\/p>\n

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

Capacitor C<\/span><\/span>1<\/span><\/sub> = <\/span><\/span>1<\/span><\/span>0<\/span><\/span> \u03bc<\/span><\/span>F = <\/span><\/span>1<\/span><\/span>0 x 10<\/span><\/span>-6<\/span><\/span><\/sup> F<\/span><\/span><\/p>\n

Capacitor C<\/span><\/span>2<\/span><\/sub> = <\/span><\/span>2<\/span><\/span>0<\/span><\/span> \u03bc<\/span><\/span>F = <\/span><\/span>2<\/span><\/span>0 x 10<\/span><\/span>-6<\/span><\/span><\/sup> F<\/span><\/span><\/p>\n

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

Wanted :<\/u><\/span><\/span> the charge on capacitor C<\/span><\/span>1<\/sub> <\/span><\/span>(Q<\/span><\/span>1<\/span><\/sub>)<\/span><\/span><\/p>\n

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

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

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

1\/C = 1\/10 + 1\/20 = 2\/20 + 1\/20 = 3\/20<\/span><\/span><\/p>\n

C = 20\/3 <\/span><\/span>\u03bc<\/span><\/span>F = (20\/3) <\/span><\/span>x <\/span><\/span>10<\/span><\/span>-6<\/span><\/span><\/sup> F<\/span><\/span><\/p>\n

Electric charge<\/a> on the equivalent capacitor :<\/span><\/span><\/p>\n

Q<\/span><\/span> = (C)(V) = (20\/3)(12)(10<\/span><\/span>-6<\/span><\/span><\/sup>) = 80 x 10<\/span><\/span>-6 <\/span><\/span><\/sup>C<\/span><\/span><\/p>\n

Q = 80 <\/span><\/span>\u03bc<\/span><\/span>C <\/span><\/span><\/p>\n

Capacitors are connected in series<\/a> so that electric charge on the equivalent capacitors = electric charge on capacitor <\/span><\/span>C<\/span><\/span>1<\/span><\/span><\/sub> = <\/span><\/span>electric charge on capacitor <\/span><\/span>C<\/span><\/span>2<\/span><\/sub>.<\/span><\/span><\/p>\n

The electric charge on capacitor <\/span><\/span>C<\/span><\/span>1<\/span><\/sub> is 80 <\/span><\/span>\u03bc<\/span><\/span>C.<\/span><\/span><\/p>\n

<\/p>\n

3. <\/span><\/span>Two capacitors, C<\/span><\/span>1<\/span><\/sub> = 2 <\/span><\/span>\u03bc<\/span><\/span>F and C<\/span><\/span>2<\/span><\/sub> = 4 <\/span><\/span>\u03bcF, <\/span><\/span>are connected in series. The capacitors are charged. The potential difference on capacitor C<\/span><\/span>1 <\/span><\/sub>is 2 Volt. The electric charge on capacitor C<\/span><\/span>2<\/span><\/sub> is…<\/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> = 2 <\/span><\/span>\u03bc<\/span><\/span>F = 2 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> = 4 <\/span><\/span>\u03bc<\/span><\/span>F = 4 x 10<\/span><\/span>-6<\/span><\/span><\/sup> F<\/span><\/span><\/p>\n

The potential difference on capacitor <\/span><\/span>C<\/span><\/span>1<\/span><\/sub> (V<\/span><\/span>1<\/span><\/sub>) = 2 Volt<\/span><\/span><\/p>\n

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

Solution :<\/span><\/span><\/u><\/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> = (2 x 10<\/span><\/span>-6<\/span><\/span><\/sup>)(2) = 4 x 10<\/span><\/span>-6 <\/span><\/span><\/sup>C<\/span><\/span><\/p>\n

Q<\/span><\/span>1<\/span><\/sub> = 4 <\/span><\/span>\u03bc<\/span><\/span>C <\/span><\/span><\/p>\n

Capacitors are connected series so that electric charge on capacitor <\/span><\/span>C<\/span><\/span>1<\/span><\/sub> = <\/span><\/span>electric charge on capacitor <\/span><\/span>C<\/span><\/span>2<\/span><\/sub>. <\/span><\/span><\/p>\n

The charge on capacitor <\/span><\/span>C<\/span><\/span>2<\/span><\/sub> is <\/span><\/span>4 <\/span><\/span>\u03bc<\/span><\/span>C. <\/span><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

1. Four capacitors, C1 = 2 \u03bcF, C2 = 1 \u03bcF, C3 = 3 \u03bcF, C4 = 4 \u03bcF, are connected in series. 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},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","jetpack_post_was_ever_published":false},"categories":[3],"tags":[],"class_list":["post-1398","post","type-post","status-publish","format-standard","hentry","category-solved-problems-in-basic-physics"],"jetpack_featured_media_url":"","jetpack-related-posts":[],"jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/1398","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=1398"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/1398\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=1398"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=1398"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=1398"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}