{"id":2733,"date":"2024-08-25T11:04:08","date_gmt":"2024-08-25T11:04:08","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=2733"},"modified":"2024-08-25T11:04:09","modified_gmt":"2024-08-25T11:04:09","slug":"ac-circuit-containing-resistance-only","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/08\/25\/ac-circuit-containing-resistance-only\/","title":{"rendered":"AC CIRCUIT CONTAINING RESISTANCE ONLY"},"content":{"rendered":"\n

The circuit containing a pure resistance of\u00a0R<\/em>\u00a0\u03a9 is shown in\u00a0Figure 7.1. Let the alternating voltage applied across the circuit be given by the equation;<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Fig. 7.1<\/strong>  Circuit containing resistance only<\/p>\n\n\n\n

\u03bd<\/em> = V<\/em>m<\/sub> sin \u03c9<\/em> t        <\/em>(7.1)<\/p>\n\n\n\n

Then, the instantaneous value of current flowing through the resistor will be;<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

The value of current will be maximum when<\/p>\n\n\n\n

 <\/p>\n\n\n\n

\u03c9<\/em> t<\/em> = 90\u00b0   or   sin \u03c9<\/em> t<\/em> = 1<\/p>\n\n\n\n

I<\/em>m<\/sub> = V<\/em>m<\/sub>\/R<\/em><\/p>\n\n\n\n

Substituting this value in\u00a0equation (7.2), we get<\/p>\n\n\n\n

i<\/em> = I<\/em>m<\/sub> sin \u03c9<\/em> t<\/em>        (7.3)<\/p>\n\n\n\n

7.2.1  Phase Angle<\/h4>\n\n\n\n

From\u00a0Equations (7.1)\u00a0and\u00a0(7.3), it is clear that there is no phase difference between the applied voltage and the current flowing through pure resistive circuit, that is, phase angle between the voltage and the current is zero. The phasor diagram and wave diagram are shown in\u00a0Figure 7.2(a)\u00a0and\u00a0(b), respectively.<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Fig. 7.2  <\/strong>(a) Phasor diagram (b) Wave diagram for voltage, current and power<\/p>\n\n\n\n

Hence, in an AC circuit containing pure resistance, current is in phase with the voltage.<\/p>\n\n\n\n

7.2.2  Power<\/h4>\n\n\n\n

Instantaneous power, p <\/em>= vi<\/em> = (V<\/em>m<\/sub> sin \u03c9<\/em> t<\/em>) (I<\/em>m<\/sub> sin \u03c9<\/em> t<\/em>)<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n
\"image\"\/<\/figure>\n\n\n\n

Average power consumed in the circuit over a complete cycle:<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

or<\/p>\n\n\n\n

 <\/p>\n\n\n\n

P = V<\/em>rms<\/sub> I<\/em>rms<\/sub> \u2212 0 or P<\/em> = VI<\/em><\/p>\n\n\n\n

7.2.3  Power Curve<\/h4>\n\n\n\n

Figure 7.2(b)\u00a0shows the power curve for a pure resistive circuit. Points on the power curve are obtained from the product of the corresponding instantaneous values of voltage and current.<\/p>\n","protected":false},"excerpt":{"rendered":"

The circuit containing a pure resistance of\u00a0R\u00a0\u03a9 is shown in\u00a0Figure 7.1. Let the alternating voltage applied across the circuit be given by the equation; Fig. 7.1  Circuit containing resistance only \u03bd = Vm sin \u03c9 t        (7.1) Then, the instantaneous value of current flowing through the resistor will be; The value of current will be maximum when   \u03c9 t = 90\u00b0   or   sin \u03c9 t = 1 Im = Vm\/R […]<\/p>\n","protected":false},"author":1,"featured_media":2481,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[410],"tags":[],"class_list":["post-2733","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-single-phase-ac-circuits"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/08\/singlephase-network-energy-meter-connection-260nw-2444369485.jpg","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2733","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/comments?post=2733"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2733\/revisions"}],"predecessor-version":[{"id":2734,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2733\/revisions\/2734"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/2481"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=2733"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=2733"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=2733"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}