{"id":2715,"date":"2024-08-24T21:06:50","date_gmt":"2024-08-24T21:06:50","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=2715"},"modified":"2024-08-24T21:06:50","modified_gmt":"2024-08-24T21:06:50","slug":"torque-equation","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/08\/24\/torque-equation\/","title":{"rendered":"\u00a0\u00a0TORQUE EQUATION"},"content":{"rendered":"\n

We know that when a current carrying conductor is placed in the magnetic field, a force is exerted on it that exerts turning moment or torque (F<\/em>\u00a0\u00d7\u00a0r<\/em>) (see\u00a0Fig. 11.38). This torque is produced due to electromagnetic effect, and hence it is called electromagnetic torque.<\/p>\n\n\n\n

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

Fig. 11.38<\/strong>  Force exerted on a single conductor<\/p>\n\n\n\n

<\/a>Let P<\/em> = number of poles<\/p>\n\n\n\n

\u0278<\/em> = flux per pole in Wb<\/p>\n\n\n\n

r<\/em> = average radius of armature in metre<\/p>\n\n\n\n

l<\/em> = effective length of each conductor in metre<\/p>\n\n\n\n

Z<\/em> = total armature conductors<\/p>\n\n\n\n

I<\/em>a<\/sub> = total armature current<\/p>\n\n\n\n

A<\/em> = number of parallel paths<\/p>\n\n\n\n

Average force on each conductor, F<\/em> = Bil<\/em> Newton<\/p>\n\n\n\n

Torque due to one conductor = F<\/em> \u00d7 r<\/em> Newton metre<\/p>\n\n\n\n

Total torque developed in the armature, T<\/em> = ZFr<\/em> Newton metre<\/p>\n\n\n\n

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

 <\/p>\n\n\n\n

T<\/em> = ZBilr<\/em>        (11.1)<\/p>\n\n\n\n

Now, current in each conductor, i<\/em> = I<\/em>a<\/sub>\/A<\/em><\/p>\n\n\n\n

Average flux density, B<\/em> = \u0278\/<\/em>a<\/em><\/p>\n\n\n\n

where \u2018a<\/em>\u2019 is the X-sectional area of flux path at radius r.<\/em><\/p>\n\n\n\n

Obviously,<\/p>\n\n\n\n

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

Substituting these values in Equation (11.1)<\/a>, we get<\/p>\n\n\n\n

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

Alternately, the power developed in the armature is given as<\/p>\n\n\n\n

 <\/p>\n\n\n\n

EI<\/em>a<\/sub> = \u03c9<\/em>T<\/em><\/p>\n\n\n\n

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

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

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

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

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

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

For a particular machine, the number of poles (P<\/em>) and number of conductors per parallel path (Z<\/em>\/A<\/em>) are constant.<\/p>\n\n\n\n

Therefore,<\/p>\n\n\n\n

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

The constant K<\/em> for a given machine is the same for the emf equation as well as for the torque equation.<\/p>\n\n\n\n

Further, T<\/em> = K2<\/sub> \u0278I<\/em>a<\/sub> , where \"image\" is another constant. Thus, T<\/em> \u221d \u0278 I<\/em>a<\/sub><\/p>\n\n\n\n

Thus, we conclude that torque produced in the armature is directly proportional to flux per pole and armature current. Moreover, the direction of electromagnetic torque developed in the armature depends upon the direction of flux or magnetic field and the direction of flow of current in armature conductors. If either of the two is reversed, the direction of torque produced is reversed, and hence, the direction of rotation. However, when both are reversed, the direction of torque does not change.<\/p>\n","protected":false},"excerpt":{"rendered":"

We know that when a current carrying conductor is placed in the magnetic field, a force is exerted on it that exerts turning moment or torque (F\u00a0\u00d7\u00a0r) (see\u00a0Fig. 11.38). This torque is produced due to electromagnetic effect, and hence it is called electromagnetic torque. Fig. 11.38  Force exerted on a single conductor Let P = number of poles […]<\/p>\n","protected":false},"author":1,"featured_media":2709,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[414],"tags":[],"class_list":["post-2715","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-dc-machines-generators-and-motors"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/08\/dc.png","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2715","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=2715"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2715\/revisions"}],"predecessor-version":[{"id":2716,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2715\/revisions\/2716"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/2709"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=2715"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=2715"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=2715"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}