{"id":52401,"date":"2024-04-15T23:38:49","date_gmt":"2024-04-15T23:38:49","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=52401"},"modified":"2024-04-15T23:38:49","modified_gmt":"2024-04-15T23:38:49","slug":"if-the-laplace-transform-of-a-signal-yt-is-yleft-s-right-1-over-sleft-s-1-right-then-its-final-value-is","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/if-the-laplace-transform-of-a-signal-yt-is-yleft-s-right-1-over-sleft-s-1-right-then-its-final-value-is\/","title":{"rendered":"If the Laplace transform of a signal y(t) is $$Y\\left( s \\right) = {1 \\over {s\\left( {s &#8211; 1} \\right)}},$$ then its final value is"},"content":{"rendered":"<p>[amp_mcq option1=&#8221;-1&#8243; option2=&#8221;0&#8243; option3=&#8221;1&#8243; option4=&#8221;Unbounded&#8221; correct=&#8221;option3&#8243;]<!--more--><\/p>\n<p>The correct answer is $\\boxed{\\text{C}}$.<\/p>\n<p>The final value theorem states that the final value of a system is equal to the limit of its Laplace transform as $s$ approaches infinity, provided that the limit exists. In this case, we have<\/p>\n<p>$$\\lim_{s \\to \\infty} Y\\left( s \\right) = \\lim_{s \\to \\infty} {1 \\over {s\\left( {s &#8211; 1} \\right)}} = \\lim_{s \\to \\infty} {1 \\over s} \\cdot \\lim_{s \\to \\infty} {1 \\over {s &#8211; 1}} = 0 \\cdot 1 = 0.$$<\/p>\n<p>Therefore, the final value of the signal is $0$.<\/p>\n<p>Option A is incorrect because the final value of the signal is not $-1$.<\/p>\n<p>Option B is incorrect because the final value of the signal is not $0$.<\/p>\n<p>Option D is incorrect because the final value of the signal is bounded.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>[amp_mcq option1=&#8221;-1&#8243; option2=&#8221;0&#8243; option3=&#8221;1&#8243; option4=&#8221;Unbounded&#8221; correct=&#8221;option3&#8243;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[959],"tags":[],"class_list":["post-52401","post","type-post","status-publish","format-standard","hentry","category-signal-processing","no-featured-image-padding"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>If the Laplace transform of a signal y(t) is $$Y\\left( s \\right) = {1 \\over {s\\left( {s - 1} \\right)}},$$ then its final value is<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/if-the-laplace-transform-of-a-signal-yt-is-yleft-s-right-1-over-sleft-s-1-right-then-its-final-value-is\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If the Laplace transform of a signal y(t) is $$Y\\left( s \\right) = {1 \\over {s\\left( {s - 1} \\right)}},$$ then its final value is\" \/>\n<meta property=\"og:description\" content=\"[amp_mcq option1=&#8221;-1&#8243; 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