{"id":633,"date":"2023-02-26T09:22:44","date_gmt":"2023-02-26T09:22:44","guid":{"rendered":"https:\/\/www.matematikazavsicki.com\/en\/?p=633"},"modified":"2023-02-26T09:22:45","modified_gmt":"2023-02-26T09:22:45","slug":"the-total-resistance-in-a-parallel-circuit","status":"publish","type":"post","link":"https:\/\/www.matematikazavsicki.com\/en\/the-total-resistance-in-a-parallel-circuit\/","title":{"rendered":"The total resistance in a parallel circuit"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">How can the total electrical resistance in a parallel circuit be calculated? Below, you can see examples of a parallel current circuit containing three parallel connected consumers with different electrical resistance. For this circuit, you can see the calculation of its total resistance. This calculation is on a page using a formula for calculating total resistance.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">The formula for total resistance in a parallel circuit<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Calculating total electrical resistance in a parallel circuit is more complicated than calculating <a href=\"https:\/\/www.matematikazavsicki.com\/en\/resistance-in-a-series-circuit\/\">total electrical resistance in a series circuit<\/a>! The formula (in case there are three consumers (resistors)  in the parallel circuit) is:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"110\" src=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/02\/Formula-for-total-electrical-resistance-in-a-parallel-circuit.jpg\" alt=\"Formula for total electrical resistance in a parallel circuit\" class=\"wp-image-638\"\/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">If the circuit has more than three consumers, then in the formula we just add their reciprocal values as a new addition in the sequence that follows.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">It is seen from the formula that the reciprocal value of the total (equivalent) electrical resistance in parallel connection is the sum of the reciprocal values of the individual electrical resistances that the circuit contains.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To solve a problem of this type you must know all about adding fractions!<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">An example of total resistance in a parallel circuit<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Below you have a fully solved example! It determines the total electrical resistance in a circuit containing only parallel connected consumers!<\/p>\n\n\n\n<p class=\"has-vivid-purple-color has-text-color wp-block-paragraph\">Example 1: Calculate the total (equivalent) electrical resistance of the circuit shown in the image below!<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"960\" height=\"720\" src=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/02\/Parallel-current-circuit.gif\" alt=\"Parallel current circuit\" class=\"wp-image-644\"\/><\/figure>\n\n\n\n<p class=\"has-vivid-purple-color has-text-color wp-block-paragraph\">From the figure above we see that the electrical resistances of the consumers in the circuit are 2.3 and 6 ohms. By substituting these values in the formula for calculating total electrical resistance for a parallel current circuit, the following expression is:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"249\" height=\"112\" src=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/02\/Substitution-of-electrical-resistance-values.jpg\" alt=\"Substitution of electrical resistance values\" class=\"wp-image-647\"\/><\/figure>\n<\/div>\n\n\n<p class=\"has-vivid-purple-color has-text-color wp-block-paragraph\">The numbers 2, 3, and 6 are the denominators of the various fractions in the expression above. To add these fractions we first need to determine the LCM of the numbers 2,3 and 6! Knowing that the smallest common denominator for the numbers 2,3 and 6 is the number 6, we expand all three fractions to the fraction that contains the number 6 in the denominator. The expression after expansion looks like this:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"252\" height=\"115\" src=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/02\/Calculation-of-total-resistance-in-a-parallel-current-circuit.jpg\" alt=\"Calculation of total resistance in a parallel current circuit\" class=\"wp-image-650\"\/><\/figure>\n<\/div>\n\n\n<p class=\"has-vivid-purple-color has-text-color wp-block-paragraph\">Now that all the fractions have the same denominator, we can easily add them, which gives us the next step:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"129\" height=\"116\" src=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/02\/Reciprocal-value-solution.jpg\" alt=\"Reciprocal value - solution\" class=\"wp-image-651\"\/><\/figure>\n<\/div>\n\n\n<p class=\"has-vivid-purple-color has-text-color wp-block-paragraph\">Finally, although the expression can be solved in several ways (by proportion, cross multiplication, etc.), to get only the total resistance on the left side instead of the reciprocal value of the total resistance, it is enough to turn the fractions on both sides upside down in the direction numerator-denominator. This gives you the solution itself:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"141\" height=\"113\" src=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/02\/Final-value.jpg\" alt=\"Final value\" class=\"wp-image-653\"\/><\/figure>\n<\/div>\n\n\n<p class=\"has-vivid-purple-color has-text-color wp-block-paragraph\">It is already clear that the total electrical resistance for the circuit of example 1 is 1 ohm!<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Video examples<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The video below contains an example of total electrical resistance in a parallel circuit!<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/youtu.be\/oldtkbn-h6Y\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"636\" height=\"357\" src=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/02\/Resistance-in-a-parallel-circuit.jpg\" alt=\"\" class=\"wp-image-659\" srcset=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/02\/Resistance-in-a-parallel-circuit.jpg 636w, https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/02\/Resistance-in-a-parallel-circuit-300x168.jpg 300w, https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/02\/Resistance-in-a-parallel-circuit-624x350.jpg 624w\" sizes=\"auto, (max-width: 636px) 100vw, 636px\" \/><\/a><\/figure>\n<\/div>\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n<form role=\"search\" method=\"get\" action=\"https:\/\/www.matematikazavsicki.com\/en\/\" class=\"wp-block-search__button-outside wp-block-search__text-button wp-block-search\"    ><label class=\"wp-block-search__label\" for=\"wp-block-search__input-1\" >Enter the mathematical term you want to explore!<\/label><div class=\"wp-block-search__inside-wrapper\" ><input class=\"wp-block-search__input\" id=\"wp-block-search__input-1\" placeholder=\"What do you want to study?\" value=\"\" type=\"search\" name=\"s\" required \/><button aria-label=\"Search\" class=\"wp-block-search__button wp-element-button\" type=\"submit\" >Search<\/button><\/div><\/form>\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">Also, follow the information and materials that will be deliver in the future. 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Below, you can see examples of a parallel current circuit containing three parallel connected consumers with different electrical [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":664,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8,6,7,18],"tags":[78,42,68,97,76,75],"class_list":["post-633","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-10th-grade","category-8th-grade","category-9th-grade","category-physics","tag-circuit","tag-examples","tag-formula","tag-parallel","tag-resistance","tag-total"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The total resistance in a parallel circuit - Math For All<\/title>\n<meta name=\"description\" content=\"How can the total electrical resistance in a parallel circuit be calculated? 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