{"id":3100,"date":"2018-06-09T13:29:25","date_gmt":"2018-06-09T20:29:25","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=3100"},"modified":"2018-06-09T13:29:25","modified_gmt":"2018-06-09T20:29:25","slug":"electromagnetic-induction-induced-emf-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/electromagnetic-induction-induced-emf-problems-and-solutions.htm","title":{"rendered":"Electromagnetic induction Induced EMF \u2013 Problems and Solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

3 Electromagnetic induction Induced EMF \u2013 Problems and Solutions<\/strong><\/p>\n

1. A coil replaced with another coil that has loops 2 times the initial loops and the rate of change of magnetic flux is constant. Determine the ratio of initial and final induced emf. <\/span><\/span><\/p>\n

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

Initial loops (N) = 1<\/span><\/span><\/p>\n

Final loops (N) = 2<\/span><\/span><\/p>\n

The rate of change of initial magnetic flux (\u0394\u00d8<\/span><\/span>B <\/span><\/span><\/sub>\/ \u0394t) = the rate of change of final magnetic flux (\u0394\u00d8<\/span><\/span>B <\/span><\/span><\/sub>\/ \u0394t)<\/span><\/span><\/p>\n

Wanted:<\/u><\/span><\/span> The ratio of initial and final induced emf<\/a><\/span><\/span><\/p>\n

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

The equation of Faraday’s law of induction :<\/u><\/span><\/span><\/p>\n

E = -N (\u0394\u00d8<\/span><\/span>B <\/span><\/span><\/sub>\/ \u0394t)<\/span><\/span><\/p>\n

E = induced EMF, N = number of loops, \u0394\u00d8<\/i><\/span><\/span>B <\/i><\/span><\/span><\/sub>\/ \u0394t = the rate of change of magnetic flux<\/i><\/span><\/span><\/p>\n

The ratio of initial and final induced emf :<\/u><\/span><\/span><\/p>\n

E initial: E final<\/span><\/span><\/p>\n

-N (\u0394\u00d8<\/span><\/span>B <\/span><\/span><\/sub>\/ \u0394t) : -N (\u0394\u00d8<\/span><\/span>B <\/span><\/span><\/sub>\/ \u0394t)<\/span><\/span><\/p>\n

1: 2<\/span><\/span><\/p>\n

2. In the initial state (1), the magnetic flux is changed by 5 Wb in 2 seconds on a coil with 20 loops. In the final state (2), the same flux changed in 8 seconds. Determine the ratio of the initially induced emf and the final induced emf.<\/span><\/span><\/p>\n

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

The rate of change of initial magnetic flux (\u0394\u00d8<\/span><\/span>B <\/span><\/span><\/sub>\/ \u0394t) = 5\/2<\/span><\/span><\/p>\n

The rate of change of final magnetic flux (\u0394\u00d8<\/span><\/span>B <\/span><\/span><\/sub>\/ \u0394t) = 5\/8 <\/span><\/span><\/p>\n

Number of loops (N) = 20<\/span><\/span><\/p>\n

Wanted:<\/u><\/span><\/span> The ratio of the initially induced emf and the final induced emf<\/span><\/span><\/p>\n

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

E initial: E final<\/span><\/span><\/p>\n

-N (\u0394\u00d8<\/span><\/span>B <\/span><\/span><\/sub>\/ \u0394t) : -N (\u0394\u00d8<\/span><\/span>B <\/span><\/span><\/sub>\/ \u0394t)<\/span><\/span><\/p>\n

20 (5\/2) : 20 (5\/8)<\/span><\/span><\/p>\n

5\/2: 5\/8<\/span><\/span><\/p>\n

1\/1: 1\/4<\/span><\/span><\/p>\n

4: 1<\/span><\/span><\/p>\n

3. The magnetic flux of the initial coil has 200 loops changes by 0.06 Wb in 0.4 seconds. The magnetic flux of the final coil has 0.08 Wb in 0.2 seconds. If several loops of the final coils are substituted with the half number of the first coil’s loops, determine the ratio of the induced emf of the initial loops and the final loops.<\/span><\/span><\/p>\n

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

The rate of change of initial magnetic flux (\u0394\u00d8<\/span><\/span>B <\/span><\/span><\/sub>\/ \u0394t) = 0.06 \/ 0.4<\/span><\/span><\/p>\n

Number of initial loops (N) = 200<\/span><\/span><\/p>\n

The rate of change of final magnetic flux (\u0394\u00d8<\/span><\/span>B <\/span><\/span><\/sub>\/ \u0394t) = 0.08 \/ 0.2<\/span><\/span><\/p>\n

Number of final loops (N) = 100<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> The ratio of the initial induced emf and the final induced emf<\/span><\/span><\/p>\n

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

E initial : E final<\/span><\/span><\/p>\n

-N (\u0394\u00d8<\/span><\/span>B <\/span><\/span><\/sub>\/ \u0394t) : -N (\u0394\u00d8<\/span><\/span>B <\/span><\/span><\/sub>\/ \u0394t)<\/span><\/span><\/p>\n

200 (0.06\/0.4) : 100 (0.08\/0.2)<\/span><\/span><\/p>\n

2 (0.15) : 1 (0.4)<\/span><\/span><\/p>\n

0.3 : 0.4<\/span><\/span><\/p>\n

3 : 4<\/span><\/span><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"

3 Electromagnetic induction Induced EMF \u2013 Problems and Solutions 1. A coil replaced with another coil that has loops 2 times the initial loops and the rate of change of magnetic flux is constant. Determine the ratio of initial and final induced emf. Known : Initial loops (N) = 1 Final loops (N) = 2 … 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":"Electromagnetic induction induced EMF \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-3100","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\/3100","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=3100"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/3100\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=3100"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=3100"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=3100"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}