{"id":85375,"date":"2025-06-01T03:14:54","date_gmt":"2025-06-01T03:14:54","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=85375"},"modified":"2025-06-01T03:14:54","modified_gmt":"2025-06-01T03:14:54","slug":"three-resistors-of-resistances-11-omega-22-omega-and-33-omega","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/three-resistors-of-resistances-11-omega-22-omega-and-33-omega\/","title":{"rendered":"Three resistors of resistances 11 $\\Omega$, 22 $\\Omega$ and 33 $\\Omega"},"content":{"rendered":"

Three resistors of resistances 11 $\\Omega$, 22 $\\Omega$ and 33 $\\Omega$ are connected in parallel. Their equivalent resistance is equal to<\/p>\n

[amp_mcq option1=”66 $\\Omega$” option2=”22 $\\Omega$” option3=”12 $\\Omega$” option4=”6 $\\Omega$” correct=”option4″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CDS-1 – 2023<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe equivalent resistance ($R_{eq}$) of resistors connected in parallel is given by the formula:
\n$1\/R_{eq} = 1\/R_1 + 1\/R_2 + 1\/R_3 + …$
\nGiven resistances are $R_1 = 11 \\, \\Omega$, $R_2 = 22 \\, \\Omega$, and $R_3 = 33 \\, \\Omega$.
\n$1\/R_{eq} = 1\/11 + 1\/22 + 1\/33$
\nTo add these fractions, find a common denominator, which is 66.
\n$1\/R_{eq} = (6 \\times 1)\/(6 \\times 11) + (3 \\times 1)\/(3 \\times 22) + (2 \\times 1)\/(2 \\times 33)$
\n$1\/R_{eq} = 6\/66 + 3\/66 + 2\/66$
\n$1\/R_{eq} = (6 + 3 + 2) \/ 66 = 11 \/ 66$
\n$R_{eq} = 66 \/ 11 = 6 \\, \\Omega$.
\n<\/section>\n
\n– For resistors in parallel, the reciprocal of the equivalent resistance is the sum of the reciprocals of individual resistances.
\n– The equivalent resistance in a parallel circuit is always less than the smallest individual resistance. In this case, 6 $\\Omega$ is less than 11 $\\Omega$.
\n<\/section>\n
\nResistors can be connected in two main ways: series and parallel. In a series connection, resistances add up ($R_{eq} = R_1 + R_2 + R_3 + …$). In a parallel connection, the voltage across each resistor is the same, and the total current is the sum of currents through each resistor.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

Three resistors of resistances 11 $\\Omega$, 22 $\\Omega$ and 33 $\\Omega$ are connected in parallel. Their equivalent resistance is equal to [amp_mcq option1=”66 $\\Omega$” option2=”22 $\\Omega$” option3=”12 $\\Omega$” option4=”6 $\\Omega$” correct=”option4″] This question was previously asked in UPSC CDS-1 – 2023 Download PDFAttempt Online The equivalent resistance ($R_{eq}$) of resistors connected in parallel is given … <\/p>\n

Detailed SolutionThree resistors of resistances 11 $\\Omega$, 22 $\\Omega$ and 33 $\\Omega<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1087],"tags":[1105,1201,1128],"class_list":["post-85375","post","type-post","status-publish","format-standard","hentry","category-upsc-cds-1","tag-1105","tag-electric-current","tag-physics","no-featured-image-padding"],"yoast_head":"\nThree resistors of resistances 11 $\\Omega$, 22 $\\Omega$ and 33 $\\Omega<\/title>\n<meta name=\"description\" content=\"The equivalent resistance ($R_{eq}$) of resistors connected in parallel is given by the formula: $1\/R_{eq} = 1\/R_1 + 1\/R_2 + 1\/R_3 + ...$ Given resistances are $R_1 = 11 , Omega$, $R_2 = 22 , Omega$, and $R_3 = 33 , Omega$. $1\/R_{eq} = 1\/11 + 1\/22 + 1\/33$ To add these fractions, find a common denominator, which is 66. $1\/R_{eq} = (6 times 1)\/(6 times 11) + (3 times 1)\/(3 times 22) + (2 times 1)\/(2 times 33)$ $1\/R_{eq} = 6\/66 + 3\/66 + 2\/66$ $1\/R_{eq} = (6 + 3 + 2) \/ 66 = 11 \/ 66$ $R_{eq} = 66 \/ 11 = 6 , Omega$. - For resistors in parallel, the reciprocal of the equivalent resistance is the sum of the reciprocals of individual resistances. - The equivalent resistance in a parallel circuit is always less than the smallest individual resistance. In this case, 6 $Omega$ is less than 11 $Omega$.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/three-resistors-of-resistances-11-omega-22-omega-and-33-omega\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Three resistors of resistances 11 $\\Omega$, 22 $\\Omega$ and 33 $\\Omega\" \/>\n<meta property=\"og:description\" content=\"The equivalent resistance ($R_{eq}$) of resistors connected in parallel is given by the formula: $1\/R_{eq} = 1\/R_1 + 1\/R_2 + 1\/R_3 + ...$ Given resistances are $R_1 = 11 , Omega$, $R_2 = 22 , Omega$, and $R_3 = 33 , Omega$. $1\/R_{eq} = 1\/11 + 1\/22 + 1\/33$ To add these fractions, find a common denominator, which is 66. $1\/R_{eq} = (6 times 1)\/(6 times 11) + (3 times 1)\/(3 times 22) + (2 times 1)\/(2 times 33)$ $1\/R_{eq} = 6\/66 + 3\/66 + 2\/66$ $1\/R_{eq} = (6 + 3 + 2) \/ 66 = 11 \/ 66$ $R_{eq} = 66 \/ 11 = 6 , Omega$. - For resistors in parallel, the reciprocal of the equivalent resistance is the sum of the reciprocals of individual resistances. - The equivalent resistance in a parallel circuit is always less than the smallest individual resistance. In this case, 6 $Omega$ is less than 11 $Omega$.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/three-resistors-of-resistances-11-omega-22-omega-and-33-omega\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T03:14:54+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Three resistors of resistances 11 $\\Omega$, 22 $\\Omega$ and 33 $\\Omega","description":"The equivalent resistance ($R_{eq}$) of resistors connected in parallel is given by the formula: $1\/R_{eq} = 1\/R_1 + 1\/R_2 + 1\/R_3 + ...$ Given resistances are $R_1 = 11 , Omega$, $R_2 = 22 , Omega$, and $R_3 = 33 , Omega$. $1\/R_{eq} = 1\/11 + 1\/22 + 1\/33$ To add these fractions, find a common denominator, which is 66. $1\/R_{eq} = (6 times 1)\/(6 times 11) + (3 times 1)\/(3 times 22) + (2 times 1)\/(2 times 33)$ $1\/R_{eq} = 6\/66 + 3\/66 + 2\/66$ $1\/R_{eq} = (6 + 3 + 2) \/ 66 = 11 \/ 66$ $R_{eq} = 66 \/ 11 = 6 , Omega$. - For resistors in parallel, the reciprocal of the equivalent resistance is the sum of the reciprocals of individual resistances. - The equivalent resistance in a parallel circuit is always less than the smallest individual resistance. In this case, 6 $Omega$ is less than 11 $Omega$.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/three-resistors-of-resistances-11-omega-22-omega-and-33-omega\/","og_locale":"en_US","og_type":"article","og_title":"Three resistors of resistances 11 $\\Omega$, 22 $\\Omega$ and 33 $\\Omega","og_description":"The equivalent resistance ($R_{eq}$) of resistors connected in parallel is given by the formula: $1\/R_{eq} = 1\/R_1 + 1\/R_2 + 1\/R_3 + ...$ Given resistances are $R_1 = 11 , Omega$, $R_2 = 22 , Omega$, and $R_3 = 33 , Omega$. $1\/R_{eq} = 1\/11 + 1\/22 + 1\/33$ To add these fractions, find a common denominator, which is 66. $1\/R_{eq} = (6 times 1)\/(6 times 11) + (3 times 1)\/(3 times 22) + (2 times 1)\/(2 times 33)$ $1\/R_{eq} = 6\/66 + 3\/66 + 2\/66$ $1\/R_{eq} = (6 + 3 + 2) \/ 66 = 11 \/ 66$ $R_{eq} = 66 \/ 11 = 6 , Omega$. - For resistors in parallel, the reciprocal of the equivalent resistance is the sum of the reciprocals of individual resistances. - The equivalent resistance in a parallel circuit is always less than the smallest individual resistance. In this case, 6 $Omega$ is less than 11 $Omega$.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/three-resistors-of-resistances-11-omega-22-omega-and-33-omega\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T03:14:54+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/three-resistors-of-resistances-11-omega-22-omega-and-33-omega\/","url":"https:\/\/exam.pscnotes.com\/mcq\/three-resistors-of-resistances-11-omega-22-omega-and-33-omega\/","name":"Three resistors of resistances 11 $\\Omega$, 22 $\\Omega$ and 33 $\\Omega","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T03:14:54+00:00","dateModified":"2025-06-01T03:14:54+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The equivalent resistance ($R_{eq}$) of resistors connected in parallel is given by the formula: $1\/R_{eq} = 1\/R_1 + 1\/R_2 + 1\/R_3 + ...$ Given resistances are $R_1 = 11 \\, \\Omega$, $R_2 = 22 \\, \\Omega$, and $R_3 = 33 \\, \\Omega$. $1\/R_{eq} = 1\/11 + 1\/22 + 1\/33$ To add these fractions, find a common denominator, which is 66. $1\/R_{eq} = (6 \\times 1)\/(6 \\times 11) + (3 \\times 1)\/(3 \\times 22) + (2 \\times 1)\/(2 \\times 33)$ $1\/R_{eq} = 6\/66 + 3\/66 + 2\/66$ $1\/R_{eq} = (6 + 3 + 2) \/ 66 = 11 \/ 66$ $R_{eq} = 66 \/ 11 = 6 \\, \\Omega$. - For resistors in parallel, the reciprocal of the equivalent resistance is the sum of the reciprocals of individual resistances. - The equivalent resistance in a parallel circuit is always less than the smallest individual resistance. In this case, 6 $\\Omega$ is less than 11 $\\Omega$.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/three-resistors-of-resistances-11-omega-22-omega-and-33-omega\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/three-resistors-of-resistances-11-omega-22-omega-and-33-omega\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/three-resistors-of-resistances-11-omega-22-omega-and-33-omega\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CDS-1","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-cds-1\/"},{"@type":"ListItem","position":3,"name":"Three resistors of resistances 11 $\\Omega$, 22 $\\Omega$ and 33 $\\Omega"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209","name":"rawan239","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","caption":"rawan239"},"sameAs":["https:\/\/exam.pscnotes.com"],"url":"https:\/\/exam.pscnotes.com\/mcq\/author\/rawan239\/"}]}},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/85375","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/comments?post=85375"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/85375\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=85375"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=85375"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=85375"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}