{"id":192504,"date":"2025-02-18T03:54:52","date_gmt":"2025-02-18T03:54:52","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=192504"},"modified":"2025-02-18T03:54:55","modified_gmt":"2025-02-18T03:54:55","slug":"an-alternating-voltage-is-given-by-v230sin314t","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/18\/an-alternating-voltage-is-given-by-v230sin314t\/","title":{"rendered":"An alternating voltage is given by V=230sin314t"},"content":{"rendered":"\n<p>An alternating voltage is given by V=230sin314t.Calculate i)frequency,ii)maximum value,iii)average value,iv)RMS value.(N\/D-2016)<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>Let&#8217;s break down the given alternating voltage equation:<\/p>\n\n\n\n<p>[<br>V = 230 \\sin(314t)<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">i) Frequency<\/h3>\n\n\n\n<p>The general form of the alternating voltage equation is:<\/p>\n\n\n\n<p>[<br>V = V_{\\text{max}} \\sin(\\omega t)<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( V_{\\text{max}} ) is the maximum voltage (230 V in this case).<\/li>\n\n\n\n<li>( \\omega ) is the angular frequency.<\/li>\n\n\n\n<li>( t ) is time.<\/li>\n<\/ul>\n\n\n\n<p>From the equation, the angular frequency ( \\omega ) is 314 radians per second. The angular frequency is related to the frequency ( f ) by the equation:<\/p>\n\n\n\n<p>[<br>\\omega = 2\\pi f<br>]<\/p>\n\n\n\n<p>So, we can calculate the frequency ( f ) as follows:<\/p>\n\n\n\n<p>[<br>314 = 2\\pi f<br>]<\/p>\n\n\n\n<p>Solving for ( f ):<\/p>\n\n\n\n<p>[<br>f = \\frac{314}{2\\pi} \\approx 50 \\, \\text{Hz}<br>]<\/p>\n\n\n\n<p>Thus, the frequency of the voltage is <strong>50 Hz<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">ii) Maximum Value (Peak Voltage)<\/h3>\n\n\n\n<p>The maximum value of the voltage is given directly in the equation as ( V_{\\text{max}} = 230 \\, \\text{V} ).<\/p>\n\n\n\n<p>Thus, the maximum value of the voltage is <strong>230 V<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">iii) Average Value<\/h3>\n\n\n\n<p>The average value of an alternating voltage over one complete cycle is given by:<\/p>\n\n\n\n<p>[<br>V_{\\text{avg}} = \\frac{2V_{\\text{max}}}{\\pi}<br>]<\/p>\n\n\n\n<p>Substituting ( V_{\\text{max}} = 230 ):<\/p>\n\n\n\n<p>[<br>V_{\\text{avg}} = \\frac{2 \\times 230}{\\pi} \\approx 146.78 \\, \\text{V}<br>]<\/p>\n\n\n\n<p>Thus, the average value of the voltage is approximately <strong>146.78 V<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">iv) RMS (Root Mean Square) Value<\/h3>\n\n\n\n<p>The RMS value of an alternating voltage is given by:<\/p>\n\n\n\n<p>[<br>V_{\\text{RMS}} = \\frac{V_{\\text{max}}}{\\sqrt{2}}<br>]<\/p>\n\n\n\n<p>Substituting ( V_{\\text{max}} = 230 ):<\/p>\n\n\n\n<p>[<br>V_{\\text{RMS}} = \\frac{230}{\\sqrt{2}} \\approx 162.63 \\, \\text{V}<br>]<\/p>\n\n\n\n<p>Thus, the RMS value of the voltage is approximately <strong>162.63 V<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Summary of Answers:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Frequency<\/strong>: 50 Hz<\/li>\n\n\n\n<li><strong>Maximum value<\/strong>: 230 V<\/li>\n\n\n\n<li><strong>Average value<\/strong>: 146.78 V<\/li>\n\n\n\n<li><strong>RMS value<\/strong>: 162.63 V<\/li>\n<\/ol>\n\n\n\n<p>Let me generate a visual representation of these values for better clarity.<\/p>\n\n\n\n<p>I wasn&#8217;t able to generate the image due to content policy guidelines. However, I can still explain how the sinusoidal waveform would look:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>maximum value<\/strong> (peak voltage) of 230 V would be the highest point on the wave.<\/li>\n\n\n\n<li>The <strong>average value<\/strong> of 146.78 V would be a horizontal line drawn through the curve that represents the average voltage over a full cycle.<\/li>\n\n\n\n<li>The <strong>RMS value<\/strong> of 162.63 V would also be marked as a reference point, showing how the waveform\u2019s effective voltage relates to a DC voltage.<\/li>\n<\/ul>\n\n\n\n<p>If you need any more help or further clarification on the graph or calculations, feel free to ask!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>An alternating voltage is given by V=230sin314t.Calculate i)frequency,ii)maximum value,iii)average value,iv)RMS value.(N\/D-2016) The Correct Answer and Explanation is : Let&#8217;s break down the given alternating voltage equation: [V = 230 \\sin(314t)] i) Frequency The general form of the alternating voltage equation is: [V = V_{\\text{max}} \\sin(\\omega t)] Where: From the equation, the angular frequency ( \\omega [&hellip;]<\/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 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