{"id":56218,"date":"2025-02-01T21:06:34","date_gmt":"2025-02-01T15:36:34","guid":{"rendered":"https:\/\/yanamtakshashila.com\/?p=56218"},"modified":"2026-02-25T04:33:23","modified_gmt":"2026-02-24T23:03:23","slug":"ex-4-i-draw-the-graphs-of-sinusoidal-waveform-of-current-and-voltage-and-ii-determine-the-root-mean-square-frequency-and-instantaneous-value-of-the-current-at-t-seconds-using-geogebra-classic-5","status":"publish","type":"post","link":"https:\/\/yanamtakshashila.com\/?p=56218","title":{"rendered":"i) Draw the graphs of sinusoidal waveform of current and voltage and ii) Determine the root mean square, frequency and instantaneous value of the current at  t seconds using geogebra classic 5 [Data Set: I_m= 110,  \u03c9 = 90,  R = 5"},"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\">\\[\\hspace{1cm}\\ \\text{The alternating current passing through a circuit is}\\ i(t)\\ =\\ I_msin\u03c9t,\\ \\hspace{10cm}\\\\ where\\ I_m\\ \\text{is the maximum value of current value of current and \u03c9 is the angular velocity.}\\ \\hspace{5cm}\\]<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\">\\[\\hspace{1cm}\\ \\text{Let R be the resistance and}\\ V_m\\ \\text{be the maximum voltage.}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[1,\\ \\text{To graph the sinusoidal waveform of i(t) for the given values of}\\ I_m\\ and\\ \u03c9.\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[2.\\ \\text{To calculate the maximum voltage}\\ V_m\\ using\\ the\\ formula\\ V_m\\ =\\ I_mR\\ \\text{for the given value of R.}\\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[3.\\ \\text{To graph the sinusoidal waveform of voltage using the formula}\\ v(t)\\ =\\ V_msin(\u03c9t  +\\ \\frac{pi}{2})\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[4.\\ \\text{To determine the value of root mean square (r.m.s) current using the formula}\\ I_{rms}\\ =\\ \\frac{I_m}{\\sqrt{2}}\\ \\hspace{5cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[5.\\ \\text{To determine the frequency using the formula}\\ F\\ =\\ \\frac{\u03c9}{2\\ \\pi}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[6.\\ \\text{To calculate the instantaneous value of the current at t = 0, 0.1,0.2,0.3,0.4 and 0.5 sec.}\\ \\hspace{5cm}\\]<\/div>\n\n\n\n<h5 class=\"wp-block-heading\">Data Set: I<sub>m <\/sub>= 110, \u03c9 = 90, R = 5<\/h5>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\"><\/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{8cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 2:}\\ \\text{To create sliders for}\\ I_m,\\  \u03c9\\ and\\ R\\ \\hspace{18cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 3:}\\ \\text{To set the sliders value for}\\ I_m\\ =\\ 110,\\  \u03c9\\ =\\ 90\\ and\\ R\\ =\\ 5\\ \\hspace{18cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 4:}\\ \\text{To view the sine waveform of the current and voltage \u2192 do the following\u2192}\\hspace{5cm}\\\\ \\hspace{1cm}\\ \\text{Graphics \u2192Preference Graphics \u2192 Basic \u2192 x Min:0, \u2192 x Max:0.5,}\\ \\hspace{5cm}\\\\ \\text{y Min:-600, y Max:600}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 5:}\\ \\text{To draw the graph of the function}\\  i(t)\\  by\\ using\\ input\\ bar\\ \\hspace{7cm}\\\\ \\text{to type}\\ i(t)\\ =\\ I_msin(\u03c9t)\\ and\\ press\\ the\\ Enter\\ key\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 6:}\\ \\text{To calculate the maximum voltage}\\  V_m\\ by\\ using\\ the\\ input\\ bar\\ \\hspace{7cm}\\\\ \\text{to type}\\ V_m\\ =\\ I_m\\ *\\ R\\ and\\ press\\ the\\ Enter\\ key\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 7:}\\ \\text{To draw the graph of the function}\\  v(t)\\  \\text{by using the input bar to type}\\ \\hspace{7cm}\\\\ \\text{v(t) = \nV_m sin(\u03c9t + pi\/2) and press Enter Key}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\"><\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 8:}\\ \\text{To determine the value of root mean square(r.m.s) current by using}\\ \\hspace{7cm}\\\\ \\text{the input bar to type I_{rms}= (I_m)\/sqrt(2) and press the Enter key}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 9:}\\ \\text{To determine the frequency by using input bar to F = \u03c9\/2 pi and press the Enter key}\\ \\hspace{5cm}\\] <\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 10:}\\ \\text{To create a slider for t with minimum = 0 and maximum = 0.5}\\ \\hspace{10cm}\\] <\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 11:}\\ \\text{To plot the variable point I on the curve i(t) by using the input bar}\\ \\hspace{7cm}\\\\ \\text{to type I = (t, i(t)) and press the Enter key}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 12:}\\ \\text{To plot the variable point V on the curve v(t) by using the input bar}\\ \\hspace{7cm}\\\\ \\text{to type V = (t, v(t)) and press the Enter key}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 13:}\\ \\text{To create an input box for t and link it with the slider for t}\\ \\hspace{10cm}\\] <\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 14:}\\ \\text{Type the values 0,0,1,0,2,0,3,0,4 and 0.5 one at a time in the}\\ \\hspace{7cm}\\\\ \\text{input box of t and record the values of I in the output field}\\ \\hspace{7cm}\\]<\/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\">Output for current and voltage<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>Description<\/td><td>Value<\/td><\/tr><tr><td>Maximum value of current (I_m)<\/td><td>110<\/td><\/tr><tr><td>Angular velocity (\u03c9)<\/td><td>90<\/td><\/tr><tr><td>Resistance (R)<\/td><td>5<\/td><\/tr><tr><td>Maximum value of voltage (V_m)<\/td><td>550<\/td><\/tr><tr><td>Root mean square current(I_rms)<\/td><td>77.78<\/td><\/tr><tr><td>Frequency (F)<\/td><td>141.37<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-text-align-center\">Output for instantaneous current for various time values<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">t<\/td><td>i(t)<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td>0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">0.1<\/td><td>45.33<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">0.2<\/td><td>&#8211; 82.61<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">0.3<\/td><td>105.2<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">0.4<\/td><td>-109.1<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">0.5<\/td><td>93.6<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n<p><iframe width=\"747\" height=\"467\" src=\"https:\/\/www.youtube.com\/embed\/qnzwnbW4yyg\" title=\"sinusoidal wave form of current and voltage using 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\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Aim: Data Set: Im = 110, \u03c9 = 90, R = 5 Procedure: Output: Output for current and voltage Description Value Maximum value of current (I_m) 110 Angular velocity (\u03c9) 90 Resistance (R) 5 Maximum value of voltage (V_m) 550 Root mean square current(I_rms) 77.78 Frequency (F) 141.37 Output for instantaneous current for various time 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