{"id":87026,"date":"2025-06-01T04:26:29","date_gmt":"2025-06-01T04:26:29","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=87026"},"modified":"2025-06-01T04:26:29","modified_gmt":"2025-06-01T04:26:29","slug":"which-one-of-the-following-expressions-has-dimensions-of-energy-here","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-expressions-has-dimensions-of-energy-here\/","title":{"rendered":"Which one of the following expressions has dimensions of energy (here"},"content":{"rendered":"

Which one of the following expressions has dimensions of energy (here V is the voltage across a resistor of resistance R and I is the current through the resistor, and t is the time)?<\/p>\n

[amp_mcq option1=”V2<\/sup> \/ I t” option2=”V2<\/sup> \/ R t” option3=”I2<\/sup> \/ R t” option4=”I2<\/sup> \/ V t” correct=”option3″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC Geoscientist – 2023<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nEnergy is defined as the capacity to do work. In electrical circuits, energy dissipated or transferred is often related to power and time. Power (P) is the rate of energy transfer, so Energy (E) = Power (P) \u00d7 time (t). For a resistor, power can be expressed as P = V\u00b2\/R or P = I\u00b2R or P = VI.
\nOption A: V\u00b2\/I t – The dimensions of V\/I are R (resistance), so V\u00b2\/I t is dimensionally (V\/I) * (V\/t) * t = R * (V\/t) * t. This doesn’t directly yield energy dimensions.
\nOption B: V\u00b2\/R t – V\u00b2\/R represents power dissipated in a resistor. Multiplying power by time (t) gives energy. Thus, (V\u00b2\/R) \u00d7 t has the dimensions of energy.
\nOption C: I\u00b2\/R t – I\u00b2R represents power dissipated in a resistor. I\u00b2\/R is dimensionally Current\u00b2 \/ Resistance, which is not power. I\u00b2R * t would be energy.
\nOption D: I\u00b2\/V t – I\u00b2\/V is dimensionally Current\u00b2 \/ Voltage. This does not represent power.
\n<\/section>\n
\n– Energy = Power \u00d7 Time.
\n– Power in a resistor = V\u00b2\/R = I\u00b2R = VI.
\n– Dimensions of Energy = [Force \u00d7 Distance] = [MLT\u207b\u00b2 \u00d7 L] = [ML\u00b2T\u207b\u00b2].
\n<\/section>\n
\nChecking dimensions formally:
\nV has dimensions [ML\u00b2I\u207b\u00b9T\u207b\u00b3]. R has dimensions [ML\u00b2I\u207b\u00b2T\u207b\u00b3]. I has dimensions [I]. t has dimensions [T].
\nOption B: (V\u00b2\/R) * t = ([ML\u00b2I\u207b\u00b9T\u207b\u00b3]\u00b2 \/ [ML\u00b2I\u207b\u00b2T\u207b\u00b3]) * [T] = ([M\u00b2L\u2074I\u207b\u00b2T\u207b\u2076] \/ [ML\u00b2I\u207b\u00b2T\u207b\u00b3]) * [T] = [ML\u00b2T\u207b\u00b3] * [T] = [ML\u00b2T\u207b\u00b2], which are the dimensions of energy.
\nOption C: (I\u00b2\/R) * t would have been energy. I\u00b2\/R * t as written in option C is [I\u00b2] \/ ([ML\u00b2I\u207b\u00b2T\u207b\u00b3] * [T]) = [I\u00b2] \/ [ML\u00b2I\u207b\u00b2T\u207b\u00b2] = [M\u207b\u00b9L\u207b\u00b2I\u2074T\u00b2].
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

Which one of the following expressions has dimensions of energy (here V is the voltage across a resistor of resistance R and I is the current through the resistor, and t is the time)? [amp_mcq option1=”V2 \/ I t” option2=”V2 \/ R t” option3=”I2 \/ R t” option4=”I2 \/ V t” correct=”option3″] This question was … <\/p>\n

Detailed SolutionWhich one of the following expressions has dimensions of energy (here<\/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":[1091],"tags":[1105,1140,1128],"class_list":["post-87026","post","type-post","status-publish","format-standard","hentry","category-upsc-geoscientist","tag-1105","tag-measurement-unit","tag-physics","no-featured-image-padding"],"yoast_head":"\nWhich one of the following expressions has dimensions of energy (here<\/title>\n<meta name=\"description\" content=\"Energy is defined as the capacity to do work. In electrical circuits, energy dissipated or transferred is often related to power and time. Power (P) is the rate of energy transfer, so Energy (E) = Power (P) \u00d7 time (t). For a resistor, power can be expressed as P = V\u00b2\/R or P = I\u00b2R or P = VI. Option A: V\u00b2\/I t - The dimensions of V\/I are R (resistance), so V\u00b2\/I t is dimensionally (V\/I) * (V\/t) * t = R * (V\/t) * t. This doesn't directly yield energy dimensions. Option B: V\u00b2\/R t - V\u00b2\/R represents power dissipated in a resistor. Multiplying power by time (t) gives energy. Thus, (V\u00b2\/R) \u00d7 t has the dimensions of energy. Option C: I\u00b2\/R t - I\u00b2R represents power dissipated in a resistor. I\u00b2\/R is dimensionally Current\u00b2 \/ Resistance, which is not power. I\u00b2R * t would be energy. Option D: I\u00b2\/V t - I\u00b2\/V is dimensionally Current\u00b2 \/ Voltage. This does not represent power. - Energy = Power \u00d7 Time. - Power in a resistor = V\u00b2\/R = I\u00b2R = VI. - Dimensions of Energy = [Force \u00d7 Distance] = [MLT\u207b\u00b2 \u00d7 L] = [ML\u00b2T\u207b\u00b2].\" \/>\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\/which-one-of-the-following-expressions-has-dimensions-of-energy-here\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Which one of the following expressions has dimensions of energy (here\" \/>\n<meta property=\"og:description\" content=\"Energy is defined as the capacity to do work. In electrical circuits, energy dissipated or transferred is often related to power and time. Power (P) is the rate of energy transfer, so Energy (E) = Power (P) \u00d7 time (t). For a resistor, power can be expressed as P = V\u00b2\/R or P = I\u00b2R or P = VI. Option A: V\u00b2\/I t - The dimensions of V\/I are R (resistance), so V\u00b2\/I t is dimensionally (V\/I) * (V\/t) * t = R * (V\/t) * t. This doesn't directly yield energy dimensions. Option B: V\u00b2\/R t - V\u00b2\/R represents power dissipated in a resistor. Multiplying power by time (t) gives energy. Thus, (V\u00b2\/R) \u00d7 t has the dimensions of energy. Option C: I\u00b2\/R t - I\u00b2R represents power dissipated in a resistor. I\u00b2\/R is dimensionally Current\u00b2 \/ Resistance, which is not power. I\u00b2R * t would be energy. Option D: I\u00b2\/V t - I\u00b2\/V is dimensionally Current\u00b2 \/ Voltage. This does not represent power. - Energy = Power \u00d7 Time. - Power in a resistor = V\u00b2\/R = I\u00b2R = VI. - Dimensions of Energy = [Force \u00d7 Distance] = [MLT\u207b\u00b2 \u00d7 L] = [ML\u00b2T\u207b\u00b2].\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-expressions-has-dimensions-of-energy-here\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T04:26:29+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=\"2 minutes\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Which one of the following expressions has dimensions of energy (here","description":"Energy is defined as the capacity to do work. In electrical circuits, energy dissipated or transferred is often related to power and time. Power (P) is the rate of energy transfer, so Energy (E) = Power (P) \u00d7 time (t). For a resistor, power can be expressed as P = V\u00b2\/R or P = I\u00b2R or P = VI. Option A: V\u00b2\/I t - The dimensions of V\/I are R (resistance), so V\u00b2\/I t is dimensionally (V\/I) * (V\/t) * t = R * (V\/t) * t. This doesn't directly yield energy dimensions. Option B: V\u00b2\/R t - V\u00b2\/R represents power dissipated in a resistor. Multiplying power by time (t) gives energy. Thus, (V\u00b2\/R) \u00d7 t has the dimensions of energy. Option C: I\u00b2\/R t - I\u00b2R represents power dissipated in a resistor. I\u00b2\/R is dimensionally Current\u00b2 \/ Resistance, which is not power. I\u00b2R * t would be energy. Option D: I\u00b2\/V t - I\u00b2\/V is dimensionally Current\u00b2 \/ Voltage. This does not represent power. - Energy = Power \u00d7 Time. - Power in a resistor = V\u00b2\/R = I\u00b2R = VI. - Dimensions of Energy = [Force \u00d7 Distance] = [MLT\u207b\u00b2 \u00d7 L] = [ML\u00b2T\u207b\u00b2].","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\/which-one-of-the-following-expressions-has-dimensions-of-energy-here\/","og_locale":"en_US","og_type":"article","og_title":"Which one of the following expressions has dimensions of energy (here","og_description":"Energy is defined as the capacity to do work. In electrical circuits, energy dissipated or transferred is often related to power and time. Power (P) is the rate of energy transfer, so Energy (E) = Power (P) \u00d7 time (t). For a resistor, power can be expressed as P = V\u00b2\/R or P = I\u00b2R or P = VI. Option A: V\u00b2\/I t - The dimensions of V\/I are R (resistance), so V\u00b2\/I t is dimensionally (V\/I) * (V\/t) * t = R * (V\/t) * t. This doesn't directly yield energy dimensions. Option B: V\u00b2\/R t - V\u00b2\/R represents power dissipated in a resistor. Multiplying power by time (t) gives energy. Thus, (V\u00b2\/R) \u00d7 t has the dimensions of energy. Option C: I\u00b2\/R t - I\u00b2R represents power dissipated in a resistor. I\u00b2\/R is dimensionally Current\u00b2 \/ Resistance, which is not power. I\u00b2R * t would be energy. Option D: I\u00b2\/V t - I\u00b2\/V is dimensionally Current\u00b2 \/ Voltage. This does not represent power. - Energy = Power \u00d7 Time. - Power in a resistor = V\u00b2\/R = I\u00b2R = VI. - Dimensions of Energy = [Force \u00d7 Distance] = [MLT\u207b\u00b2 \u00d7 L] = [ML\u00b2T\u207b\u00b2].","og_url":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-expressions-has-dimensions-of-energy-here\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T04:26:29+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-expressions-has-dimensions-of-energy-here\/","url":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-expressions-has-dimensions-of-energy-here\/","name":"Which one of the following expressions has dimensions of energy (here","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T04:26:29+00:00","dateModified":"2025-06-01T04:26:29+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"Energy is defined as the capacity to do work. In electrical circuits, energy dissipated or transferred is often related to power and time. Power (P) is the rate of energy transfer, so Energy (E) = Power (P) \u00d7 time (t). For a resistor, power can be expressed as P = V\u00b2\/R or P = I\u00b2R or P = VI. Option A: V\u00b2\/I t - The dimensions of V\/I are R (resistance), so V\u00b2\/I t is dimensionally (V\/I) * (V\/t) * t = R * (V\/t) * t. This doesn't directly yield energy dimensions. Option B: V\u00b2\/R t - V\u00b2\/R represents power dissipated in a resistor. Multiplying power by time (t) gives energy. Thus, (V\u00b2\/R) \u00d7 t has the dimensions of energy. Option C: I\u00b2\/R t - I\u00b2R represents power dissipated in a resistor. I\u00b2\/R is dimensionally Current\u00b2 \/ Resistance, which is not power. I\u00b2R * t would be energy. Option D: I\u00b2\/V t - I\u00b2\/V is dimensionally Current\u00b2 \/ Voltage. This does not represent power. - Energy = Power \u00d7 Time. - Power in a resistor = V\u00b2\/R = I\u00b2R = VI. - Dimensions of Energy = [Force \u00d7 Distance] = [MLT\u207b\u00b2 \u00d7 L] = [ML\u00b2T\u207b\u00b2].","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-expressions-has-dimensions-of-energy-here\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-expressions-has-dimensions-of-energy-here\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-expressions-has-dimensions-of-energy-here\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC Geoscientist","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-geoscientist\/"},{"@type":"ListItem","position":3,"name":"Which one of the following expressions has dimensions of energy (here"}]},{"@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\/87026","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=87026"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/87026\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=87026"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=87026"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=87026"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}