{"id":8429,"date":"2012-04-17T00:31:00","date_gmt":"2012-04-16T23:31:00","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=8429"},"modified":"2022-01-29T23:26:25","modified_gmt":"2022-01-29T23:26:25","slug":"a-diferenca-de-potencial","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=8429","title":{"rendered":"A diferen\u00e7a de potencial"},"content":{"rendered":"<p><ul id='GTTabs_ul_8429' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_8429' class='GTTabs_curr'><a  id=\"8429_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_8429' ><a  id=\"8429_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_8429'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>A\u00a0diferen\u00e7a de potencial, medida em <em>Volt<\/em>, entre dois pontos de um circuito \u00e9 dada por:<\/p>\n<p>$$u(t) = 220\\sqrt 2 \\operatorname{sen} \\left( {100\\pi t + \\frac{4}{5}\\pi } \\right)$$<\/p>\n<p>($t$ em segundos)<\/p>\n<ol>\n<li>Mostre que $\\frac{1}{{50}}$ \u00e9 per\u00edodo da fun\u00e7\u00e3o $u$.<\/li>\n<li>Represente graficamente a fun\u00e7\u00e3o $u$.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_8429' onClick='GTTabs_show(1,8429)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_8429'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Ora,\u00a0$$\\begin{array}{*{20}{l}}<br \/>\n{u\\left( {t + \\frac{1}{{50}}} \\right)}&amp; = &amp;{220\\sqrt 2 \\operatorname{sen} \\left( {100\\pi \\left( {t + \\frac{1}{{50}}} \\right) + \\frac{4}{5}\\pi } \\right)} \\\\<br \/>\n{}&amp; = &amp;{220\\sqrt 2 \\operatorname{sen} \\left( {100\\pi t + 2\\pi\u00a0 + \\frac{4}{5}\\pi } \\right)} \\\\<br \/>\n{}&amp; = &amp;{220\\sqrt 2 \\operatorname{sen} \\left( {100\\pi t + \\frac{4}{5}\\pi } \\right)} \\\\<br \/>\n{}&amp; = &amp;{u(t)}<br \/>\n\\end{array}$$<br \/>\nComo $u\\left( {t + \\frac{1}{{50}}} \\right) = u(t), \\vee t \\in {D_u}$, ent\u00e3o $\\frac{1}{{50}}$ \u00e9 per\u00edodo da fun\u00e7\u00e3o $u$.<br \/>\n\u00ad<\/li>\n<li>Apresenta-se seguidamente uma representa\u00e7\u00e3o gr\u00e1fica da fun\u00e7\u00e3o $u$.<\/li>\n<\/ol>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag41-14.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"8433\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=8433\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag41-14.jpg\" data-orig-size=\"640,405\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Gr\u00e1fico\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag41-14.jpg\" class=\"aligncenter size-full wp-image-8433\" title=\"Gr\u00e1fico\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag41-14.jpg\" alt=\"\" width=\"640\" height=\"405\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag41-14.jpg 640w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag41-14-300x189.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag41-14-150x94.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag41-14-400x253.jpg 400w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/a><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_8429' onClick='GTTabs_show(0,8429)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A\u00a0diferen\u00e7a de potencial, medida em Volt, entre dois pontos de um circuito \u00e9 dada por: $$u(t) = 220\\sqrt 2 \\operatorname{sen} \\left( {100\\pi t + \\frac{4}{5}\\pi } \\right)$$ ($t$ em segundos) Mostre&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":21089,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,295],"tags":[427,296,297],"series":[],"class_list":["post-8429","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-12--ano","category-aplicando","category-funcoes-seno-co-seno-e-tangente","tag-12-o-ano","tag-funcao-seno","tag-periodo-positivo-minimo"],"views":2630,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12V3Pag041-14_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8429","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=8429"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8429\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/21089"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8429"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8429"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8429"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=8429"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}