An inductor has an inductance of 0.025 H and a wire resistance of 3 V. How long will it take the current to reach its full Ohm’s law value?<\/p>\n\n\n\n
The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n To determine the time it takes for the current to reach its full Ohm\u2019s Law value in an inductor with resistance, we analyze the RL time constant<\/strong>.<\/p>\n\n\n\n The time constant (( \\tau )) of an RL circuit<\/strong> is given by:<\/p>\n\n\n\n [ Substituting the values:<\/p>\n\n\n\n [ In an RL circuit, the current grows according to the equation:<\/p>\n\n\n\n [ where ( I_{\\text{max}} ) is the final current given by Ohm\u2019s Law<\/strong>:<\/p>\n\n\n\n [ The current approaches 99% of its full value after about 5 time constants<\/strong>:<\/p>\n\n\n\n [ Substituting:<\/p>\n\n\n\n [ In an RL circuit, an inductor resists changes in current due to the voltage induced across it. When a voltage source is applied, the current does not instantly reach its maximum value but rather increases gradually, following an exponential curve.<\/p>\n\n\n\n The time constant ( \\tau ) represents how quickly the current rises. After one ( \\tau ), the current reaches about 63%<\/strong> of its maximum value. After about 5\u03c4 (41.7 ms in this case)<\/strong>, the current reaches 99%<\/strong> of its final value, which is practically considered “full” in electrical engineering.<\/p>\n\n\n\n Thus, in this case, the current will take approximately 41.7 milliseconds<\/strong> to reach its full Ohm\u2019s law value.<\/p>\n","protected":false},"excerpt":{"rendered":" An inductor has an inductance of 0.025 H and a wire resistance of 3 V. How long will it take the current to reach its full Ohm’s law value? The correct answer and explanation is : To determine the time it takes for the current to reach its full Ohm\u2019s Law value in an inductor […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-204845","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/204845","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=204845"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/204845\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=204845"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=204845"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=204845"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Given Data:<\/h3>\n\n\n\n
\n
Step 1: RL Circuit Time Constant<\/h3>\n\n\n\n
\\tau = \\frac{L}{R}
]<\/p>\n\n\n\n
\\tau = \\frac{0.025}{3} = 0.0083 \\text{ s} = 8.33 \\text{ ms}
]<\/p>\n\n\n\nStep 2: Current Growth in an RL Circuit<\/h3>\n\n\n\n
I(t) = I_{\\text{max}} \\left( 1 – e^{-t\/\\tau} \\right)
]<\/p>\n\n\n\n
I_{\\text{max}} = \\frac{V}{R}
]<\/p>\n\n\n\n
t \\approx 5\\tau
]<\/p>\n\n\n\n
t = 5 \\times 0.0083 = 0.0417 \\text{ s} = 41.7 \\text{ ms}
]<\/p>\n\n\n\nStep 3: Explanation<\/h3>\n\n\n\n