{"id":3136,"date":"2018-06-18T22:33:21","date_gmt":"2018-06-19T05:33:21","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=3136"},"modified":"2018-06-18T22:33:21","modified_gmt":"2018-06-19T05:33:21","slug":"lrc-series-ac-circuit-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/lrc-series-ac-circuit-problems-and-solutions.htm","title":{"rendered":"LRC Series AC Circuit \u2013 problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

1. <\/span><\/span><\/p>\n

\"LRC<\/p>\n

Determine the electric current in circuit (1 \u00b5F = 10<\/span><\/span>-6<\/span><\/span><\/sup> F) <\/span><\/span><\/p>\n

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

Resistor<\/a> (R) = 12 Ohm<\/span><\/span><\/p>\n

Inductor <\/span><\/span>(L) = 0.075 H<\/span><\/span><\/p>\n

Capacitor<\/a> (C) = 500 \u00b5F = 500 x 10<\/span><\/span>-6<\/span><\/span><\/sup> F = 5 x 10<\/span><\/span>-4<\/span><\/span><\/sup> Farad <\/span><\/span><\/p>\n

Voltage (V) = V<\/span><\/span>o<\/span><\/sub> sin \u03c9<\/span><\/span>t = <\/span><\/span>v<\/span><\/span>o<\/span><\/sub> sin 2\u03c0f<\/span><\/span>t = <\/span><\/span>26 sin 200t<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> Electric current<\/span><\/span><\/a><\/p>\n

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

Impedance (Z) :<\/u><\/span><\/span><\/p>\n

\"LRC<\/p>\n

The inductive reactance (X<\/i><\/span><\/span>L<\/i><\/span><\/sub>) = <\/i><\/span><\/span>\u03c9L = (200)(0,075) = 15 Ohm<\/i><\/span><\/span><\/p>\n

The capacitive reactance (X<\/i><\/span><\/span>C<\/i><\/span><\/sub>) = 1 \/ \u03c9C = 1 \/ (200)(5 x 10<\/i><\/span><\/span>-4<\/i><\/span><\/span><\/sup>) = 1 \/ (1000 x 10<\/i><\/span><\/span>-4<\/i><\/span><\/span><\/sup>) = 1 \/ 10<\/i><\/span><\/span>-1<\/i><\/span><\/span><\/sup> = 10<\/i><\/span><\/span>1<\/i><\/span><\/span><\/sup> = 10 Ohm <\/i><\/span><\/span><\/p>\n

Resistor (R) = 12 Ohm<\/i><\/span><\/span><\/p>\n

\"LRC<\/p>\n

Electric current (I)<\/u><\/span><\/span> :<\/span><\/span><\/p>\n

I = V \/ Z = 26 Volt \/ 13 Ohm <\/span><\/span><\/p>\n

I = 2 Volt\/Ohm<\/span><\/span><\/p>\n

I = 2 Amp<\/span><\/span><\/p>\n

2. If the impedance of the circuit is 250 \u03a9, determine the resistance of resistor R.<\/span><\/span><\/p>\n

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

The impedance of the circuit (Z) = 250 \u03a9<\/span><\/span><\/p>\n

Capacitor (C) = 8 <\/span><\/span>m<\/span><\/span> F = 8 x 10<\/span><\/span>-6<\/span><\/span><\/sup> F <\/span><\/span><\/p>\n

Inductor (L) = 0.8 H<\/span><\/span><\/p>\n

Voltage (V) = 200 Volt<\/span><\/span><\/p>\n

w<\/span><\/span> = 500 rad\/s<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> Resistance of resistor (R)<\/span><\/span><\/p>\n

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

\"LRC<\/p>\n

\"LRC<\/p>\n

3. Determine the potential difference of both edge of the inductor.<\/span><\/span><\/p>\n

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

R = 40 <\/span><\/span>W<\/span><\/span><\/p>\n

X<\/span><\/span>L <\/span><\/sub>= 150 <\/span><\/span>W<\/span><\/span><\/p>\n

X<\/span><\/span>C<\/span><\/sub>= 120 <\/span><\/span>W<\/span><\/span><\/p>\n

V = 100 Volt<\/span><\/span><\/p>\n

Wanted:<\/u><\/span><\/span> the potential difference<\/span><\/span><\/p>\n

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

The total impedance Z of the circuit :<\/span><\/span><\/p>\n

\"LRC<\/p>\n

The potential difference of both edge of the inductor :<\/span><\/span><\/p>\n

\"LRC<\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"

1. Determine the electric current in circuit (1 \u00b5F = 10-6 F)<\/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":"LRC Series AC Circuit \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-3136","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\/3136","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=3136"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/3136\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=3136"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=3136"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=3136"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}