{"id":217714,"date":"2025-05-22T11:19:26","date_gmt":"2025-05-22T11:19:26","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=217714"},"modified":"2025-05-22T11:19:28","modified_gmt":"2025-05-22T11:19:28","slug":"a-high-voltage-direct-current-generating-station-delivers-power-to-a-city","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/22\/a-high-voltage-direct-current-generating-station-delivers-power-to-a-city\/","title":{"rendered":"A high-voltage direct-current generating station delivers power to a city."},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">A high-voltage direct-current generating station delivers power to a city. The generator output voltage is V0=400 kV, the city is represented by resistance RL=3542 ohms, and each wire of the transmission line round-trip between the station and city is represented by resistance RTL=195 ohms. What is the voltage VL when the electricity reaches the city (in kilo volt)?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To find the voltage $V_L$ when the electricity reaches the city, we can use principles of <strong>voltage division<\/strong> in a <strong>series circuit<\/strong>, since the transmission line and city load resistances are in series.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Given:<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Generator voltage: $V_0 = 400 \\, \\text{kV} = 400,000 \\, \\text{V}$<\/li>\n\n\n\n<li>Load resistance (city): $R_L = 3542 \\, \\Omega$<\/li>\n\n\n\n<li>Total transmission line resistance (round-trip): $R_{TL} = 195 \\, \\Omega$<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 1: Total resistance in the circuit<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>R_{\\text{total}} = R_{L} + R_{TL} = 3542 \\, \\Omega + 195 \\, \\Omega = 3737 \\, \\Omega<br>$$<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 2: Current in the circuit<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Using Ohm\u2019s Law:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>I = \\frac{V_0}{R_{\\text{total}}} = \\frac{400000 \\, \\text{V}}{3737 \\, \\Omega} \\approx 107.09 \\, \\text{A}<br>$$<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 3: Voltage across the city load<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>V_L = I \\cdot R_L = 107.09 \\, \\text{A} \\times 3542 \\, \\Omega \\approx 379400 \\, \\text{V}<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Convert to kilovolts:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>V_L \\approx \\frac{379400}{1000} = \\boxed{379.4 \\, \\text{kV}}<br>$$<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 Final Answer: $\\boxed{379.4 \\, \\text{kV}}$<\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation (300+ words):<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">This problem illustrates the concept of <strong>voltage drop in a series circuit<\/strong> due to resistive losses along a transmission line. In long-distance power transmission, especially with <strong>high-voltage direct current (HVDC)<\/strong> systems, minimizing energy loss is crucial. Here, the generator outputs 400 kV, but due to resistance in the wires, not all of this voltage reaches the city.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The entire setup is modeled as a simple series circuit: the transmission line resistance ($R_{TL}$) and the city\u2019s electrical resistance load ($R_L$). Because current is the same through all elements in a series circuit, we can calculate the total resistance to find the current. Using Ohm\u2019s Law $(V = IR)$, the total current $I$ drawn from the generator is calculated by dividing the total voltage by the total resistance.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Once we know the current, we find how much of the generator\u2019s voltage actually drops across the city\u2019s load. Since $V = IR$, multiplying the current by $R_L$ gives us the voltage reaching the city. In this case, the city receives approximately <strong>379.4 kV<\/strong>, which means about <strong>20.6 kV is lost<\/strong> due to resistance in the wires.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This emphasizes the importance of using <strong>high voltage<\/strong> in power transmission: for the same power, higher voltages mean lower currents, and since resistive losses are proportional to the square of the current $(P = I^2R)$, they are significantly reduced. This is a fundamental principle behind HVDC systems, which are used for efficient long-distance energy transfer<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/05\/image-49.png\" alt=\"\" class=\"wp-image-217715\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>A high-voltage direct-current generating station delivers power to a city. The generator output voltage is V0=400 kV, the city is represented by resistance RL=3542 ohms, and each wire of the transmission line round-trip between the station and city is represented by resistance RTL=195 ohms. What is the voltage VL when the electricity reaches the city [&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 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-217714","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/217714","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=217714"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/217714\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=217714"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=217714"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=217714"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}