{"id":57022,"date":"2025-03-05T16:31:11","date_gmt":"2025-03-05T11:01:11","guid":{"rendered":"https:\/\/yanamtakshashila.com\/?p=57022"},"modified":"2026-02-24T21:48:08","modified_gmt":"2026-02-24T16:18:08","slug":"ex-6-complex-numbers-phasor-sum-power-factor","status":"publish","type":"post","link":"https:\/\/yanamtakshashila.com\/?p=57022","title":{"rendered":"Ex-6 &#8211; COMPLEX NUMBERS &#8211; PHASOR SUM &#8211; POWER FACTOR"},"content":{"rendered":"\n<h5 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-89bfda0d449bddcb20c4924e685a3000\">Aim:<\/h5>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\text{Do the following activities:}\\ \\hspace{25cm}\\]<script src=\"https:\/\/yanamtakshashila.com\/wp-includes\/js\/dist\/hooks.min.js?ver=dd5603f07f9220ed27f1\" id=\"wp-hooks-js\"><\/script>\n<script src=\"https:\/\/yanamtakshashila.com\/wp-includes\/js\/dist\/i18n.min.js?ver=c26c3dc7bed366793375\" id=\"wp-i18n-js\"><\/script>\n<script id=\"wp-i18n-js-after\">\nwp.i18n.setLocaleData( { 'text direction\\u0004ltr': [ 'ltr' ] } );\n\/\/# sourceURL=wp-i18n-js-after\n<\/script>\n<script  async src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-MML-AM_CHTML\" id=\"mathjax-js\"><\/script>\n<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[1.\\ \\hspace{1cm}\\ \\text{The representation of apparent power as phasor sum of}\\ \\hspace{14cm}\\\\ \\text{active power and reactive power is given by}\\ \\hspace{16cm}\\\\ \\text{S = 550 + 952.63j.}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[i.\\ \\hspace{1cm}\\ \\text{To draw the phasor diagram of the system}\\ \\hspace{12cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[ii.\\ \\hspace{1cm}\\ \\text{Find the numerical value of the apparent power,}\\ \\hspace{11cm}\\\\ \\hspace{1cm}\\ \\text{also calculate the phase angel and}\\ \\hspace{12cm}\\\\ \\hspace{1cm}\\ \\text{power factor of the system}\\  \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[2.\\ \\hspace{1cm}\\ \\text{A machine takes 10KW (real power, P) at a power factor of}\\ \\hspace{14cm}\\\\ \\text{0.6 from 400 V supply.}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[i.\\ \\hspace{1cm}\\ \\text{Calculate the total load in KVA (apparent power, S) and}\\ \\hspace{11cm}\\\\ \\hspace{1cm}\\ \\text{KVAR (reactive power, R) represent the apparent power}\\ \\hspace{12cm}\\\\ \\hspace{1cm}\\ \\text{as a phasor sum of active power and reactive power}\\  \\hspace{10cm}\\]<\/div>\n\n\n\n<h5 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-caaadd60b535c837691a2eb0c3ab170e\">Procedure:<\/h5>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 1:}\\ \\text{Open Geogebra classic 5 (by double clicking on the icon)}\\ \\hspace{18cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 2:}\\ \\text{To the representation of apparent power as phasor sum of active power and}\\ \\hspace{15cm}\\\\ \\text{reactive power is given by by S = 550 + 952.63j using the input bar to type S = 550 + 952.63i}\\ \\hspace{10cm}\\\\ \\text{and press the Enter key. change x axis (Min:0 to Max:1000) and change y axis (Min:0 to Max:1000)}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 3:}\\ \\text{To plot the points O and P by using the input bar  to type O=(0,0) and P=(550,0)}\\ \\hspace{15cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 4:}\\ \\text{To calculate the numerical value of the Apparenpower}\\ \\hspace{19cm}\\\\ \\text{by using the input bar  to type Apparentpower= segment (O, S)}\\ \\hspace{12cm}\\\\ \\text{and press the Enter key}\\ \\hspace{16cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 4:}\\ \\text{To calculate the value of the Activepower}\\ \\hspace{19cm}\\\\ \\text{by using the input bar  to type Activepower= segment (O, P)}\\ \\hspace{12cm}\\\\ \\text{and press the Enter key}\\ \\hspace{16cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 6:}\\ \\text{To calculate the value of the Reactivepower}\\ \\hspace{19cm}\\\\ \\text{by using the input bar  to type Reactivepower= segment (S, P)}\\ \\hspace{12cm}\\\\ \\text{and press the Enter key}\\ \\hspace{16cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 7:}\\ \\text{To calculate the phase angle POS}\\ \\hspace{19cm}\\\\ \\text{by using the input command Angle(P,O,S)}\\ \\text{and press the Enter key}\\ \\hspace{12cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 8:}\\ \\text{To calculate the power factor}\\ \\hspace{20cm}\\\\ \\text{by using the input bar to type cos(\u03b1)}\\ \\text{and press the Enter key}\\ \\hspace{12cm}\\]<\/div>\n\n\n\n<h5 class=\"wp-block-heading\">To evaluate the power factor.<\/h5>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 9:}\\ \\text{Open Geogebra classic 5 new Window}\\ \\hspace{19cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 10:}\\ \\text{By using input bar to type P =10 and F = 0.6}\\ \\hspace{19cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 11:}\\ \\text{To calculate the phase angel}\\ \\hspace{20cm}\\\\ \\text{by using the input bar to type \u03b1 = arccos(F)}\\ \\text{and press the Enter key}\\ \\hspace{12cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 12:}\\ \\text{By using input bar to type V = 400}\\ \\hspace{19cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 13:}\\ \\text{To calculate the value of current}\\ \\hspace{20cm}\\\\ \\text{by using the input bar to type I=P \/(V cos(\u03b1))}\\ \\text{and press the Enter key}\\ \\hspace{12cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 14:}\\ \\text{To calculate the reactive power (imaginary power)}\\ \\hspace{20cm}\\\\ \\text{by using the input bar to type R = V I sin(\u03b1)}\\ \\text{and press the Enter key}\\ \\hspace{12cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 15:}\\ \\text{To plot the phasor representation}\\ \\hspace{20cm}\\\\ \\text{by using the input bar to type S = P + Ri}\\ \\text{and press the Enter key}\\ \\hspace{12cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 16:}\\ \\text{To plot the points O and}\\ P_1\\ \\text{by using the input bar  to type O=(0,0) and}\\ P_1\\ =\\ (10,0)\\  \\hspace{15cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 17:}\\ \\text{To calculate the numerical values of the three power components}\\ \\hspace{15cm}\\\\ \\text{by using the input bar to type ApparentPower = Segment(O,S)}\\ \\text{and press the Enter key}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 18:}\\ \\text{Similarly, by using the input bar to type}\\ ActivePower\\ =\\ Segment(O,\\ P_1)\\  \\hspace{15cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 19:}\\ \\text{Similarly, by using the input bar to type}\\ ReactivePower\\ =\\ Segment(S,\\ P_1)\\  \\hspace{15cm}\\]<\/div>\n\n\n\n<h5 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-883bedab9864fd79dff46cd9aa765019\">Output:<\/h5>\n\n\n\n<p class=\"has-text-align-center has-vivid-red-color has-text-color has-link-color wp-elements-8ca308434bdec289cb91d93bfa104a96\">Output for phasor diagram of the system<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>Description<\/td><td>Value \/ Expression<\/td><\/tr><tr><td>Phasor sum<\/td><td>S=550+952.63i<\/td><\/tr><tr><td>Phasor angle<\/td><td>\u03b1 = 60<sup>0<\/sup><\/td><\/tr><tr><td>Power factor<\/td><td>a = 0.5<\/td><\/tr><tr><td>Apparent power<\/td><td>1100<\/td><\/tr><tr><td>Active power<\/td><td>550<\/td><\/tr><tr><td>Reactive power<\/td><td>952.63<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-text-align-center has-vivid-red-color has-text-color has-link-color wp-elements-18d0e75002d6cc4ce613b1710c3862d8\">Output for power factor<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>Description<\/td><td>Value \/ Expression<\/td><\/tr><tr><td>Active power (P)<\/td><td>10<\/td><\/tr><tr><td>Power factor (F)<\/td><td>0.6<\/td><\/tr><tr><td>Phase angle (\u03b1)<\/td><td>53.13<sup>0<\/sup><\/td><\/tr><tr><td>Voltage (V)<\/td><td>400<\/td><\/tr><tr><td>Current (I)<\/td><td>1\/24<\/td><\/tr><tr><td>Reactive power (R)<\/td><td>13.33<\/td><\/tr><tr><td>Phasor sum (S)<\/td><td>S=10+13.33i<\/td><\/tr><tr><td>Apparent power<\/td><td>16.67<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n<p><iframe width=\"747\" height=\"467\" src=\"https:\/\/www.youtube.com\/embed\/2bqIs-BWWjg?list=PLQIom4Rz29vxqw62b-K0UoGK5ELvoP1wd\" title=\"Phasor Sum Diagram - Complex Numbers - Geogebra classic 5 - Explained in Telugu\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen=\"\"><\/iframe><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Aim: Procedure: To evaluate the power factor. Output: Output for phasor diagram of the system Description Value \/ Expression Phasor sum S=550+952.63i Phasor angle \u03b1 = 600 Power factor a = 0.5 Apparent power 1100 Active power 550 Reactive power 952.63 Output for power factor Description Value \/ Expression Active power (P) 10 Power factor [&hellip;]<\/p>\n","protected":false},"author":187055548,"featured_media":57047,"comment_status":"open","ping_status":"open","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":"disabled","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":"set","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":""}},"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false},"version":2},"_wpas_customize_per_network":false,"jetpack_post_was_ever_published":false},"categories":[711788881],"tags":[],"class_list":["post-57022","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-applied-mathematics-ii-p"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Ex-6 - COMPLEX NUMBERS - PHASOR SUM - POWER FACTOR - YANAMTAKSHASHILA<\/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:\/\/yanamtakshashila.com\/?p=57022\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Ex-6 - COMPLEX NUMBERS - PHASOR SUM - POWER FACTOR - YANAMTAKSHASHILA\" \/>\n<meta property=\"og:description\" content=\"Aim: Procedure: To evaluate the power factor. Output: Output for phasor diagram of the system Description Value \/ Expression Phasor sum S=550+952.63i Phasor angle \u03b1 = 600 Power factor a = 0.5 Apparent power 1100 Active power 550 Reactive power 952.63 Output for power factor Description Value \/ Expression Active power (P) 10 Power factor [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/yanamtakshashila.com\/?p=57022\" \/>\n<meta property=\"og:site_name\" content=\"YANAMTAKSHASHILA\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/profile.php?id=100063680185552\" \/>\n<meta property=\"article:author\" content=\"https:\/\/www.facebook.com\/profile.php?id=100063680185552\" \/>\n<meta property=\"article:published_time\" content=\"2025-03-05T11:01:11+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-02-24T16:18:08+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/yanamtakshashila.com\/wp-content\/uploads\/2025\/03\/phasor.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1200\" \/>\n\t<meta property=\"og:image:height\" content=\"675\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"rajuviswa\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rajuviswa\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/yanamtakshashila.com\\\/?p=57022#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/yanamtakshashila.com\\\/?p=57022\"},\"author\":{\"name\":\"rajuviswa\",\"@id\":\"https:\\\/\\\/yanamtakshashila.com\\\/#\\\/schema\\\/person\\\/a990a0af264ac2298c19fa61d2bda16e\"},\"headline\":\"Ex-6 &#8211; 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