{"id":87062,"date":"2025-06-01T04:27:19","date_gmt":"2025-06-01T04:27:19","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=87062"},"modified":"2025-06-01T04:27:19","modified_gmt":"2025-06-01T04:27:19","slug":"the-i-v-graph-for-two-resistors-resistor-1-r_1-and-resistor-2","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-i-v-graph-for-two-resistors-resistor-1-r_1-and-resistor-2\/","title":{"rendered":"The $I-V$ graph for two resistors, resistor 1 ($R_1$) and resistor 2 ("},"content":{"rendered":"

The $I-V$ graph for two resistors, resistor 1 ($R_1$) and resistor 2 ($R_2$), are shown below :
\n
[Image of I-V graph]
\n
Which one of the following statements about these resistors is not correct?<\/p>\n

[amp_mcq option1=”$R_1$ follows Ohm’s law.” option2=”$R_2$ does not follow Ohm’s law after voltage $V_1$.” option3=”Up to $V_1$, the resistance of $R_1$ is smaller than that of $R_2$.” option4=”Up to $V_1$, the resistance of $R_1$ is larger than that of $R_2$.” correct=”option4″]<\/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
\nThe correct answer is D) Up to $V_1$, the resistance of $R_1$ is larger than that of $R_2$.
\n<\/section>\n
\nThe resistance $R$ of a component can be determined from its I-V graph as $R = V\/I$. This is equivalent to $R = 1 \/ (\\text{slope of the I-V graph})$ if the graph plots I on the y-axis and V on the x-axis, as shown in the image.
\nFor resistor $R_1$, the graph is a straight line passing through the origin, indicating that $R_1$ is an ohmic resistor and follows Ohm’s law. Its resistance is constant. The slope of the $R_1$ line (I\/V) is constant.
\nFor resistor $R_2$, the graph is a curve. Up to voltage $V_1$, the graph is approximately linear but less steep than $R_1$. The slope of the $R_2$ curve (I\/V) is smaller than the slope of the $R_1$ line in this region.
\nSince resistance $R = 1 \/ (\\text{slope of I-V graph})$, a smaller slope corresponds to a larger resistance.
\nComparing the slopes up to $V_1$: (Slope of $R_1$) > (Slope of $R_2$).
\nTherefore, (Resistance of $R_1$) < (Resistance of $R_2$).\nStatement A is correct because $R_1$ graph is a straight line through origin.\nStatement B is correct because the curve of $R_2$ after $V_1$ shows that its resistance (V\/I or $1\/$slope) changes (increases as V increases).\nStatement C says \"Up to $V_1$, the resistance of $R_1$ is smaller than that of $R_2$\". This is consistent with our finding that $R_1 < R_2$ up to $V_1$. So C is correct.\nStatement D says \"Up to $V_1$, the resistance of $R_1$ is larger than that of $R_2$\". This contradicts Statement C and our analysis. Therefore, Statement D is not correct.\n<\/section>\n
\nAn ohmic resistor has a constant resistance independent of the voltage or current. A non-ohmic resistor’s resistance changes with voltage or current, resulting in a curved I-V graph. The graph for $R_2$ shows increasing resistance as voltage\/current increases beyond $V_1$. This behaviour is typical of components like light bulbs where resistance increases with temperature.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

The $I-V$ graph for two resistors, resistor 1 ($R_1$) and resistor 2 ($R_2$), are shown below : [Image of I-V graph] Which one of the following statements about these resistors is not correct? [amp_mcq option1=”$R_1$ follows Ohm’s law.” option2=”$R_2$ does not follow Ohm’s law after voltage $V_1$.” option3=”Up to $V_1$, the resistance of $R_1$ is … <\/p>\n

Detailed SolutionThe $I-V$ graph for two resistors, resistor 1 ($R_1$) and resistor 2 (<\/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":[1105,1201,1128],"class_list":["post-87062","post","type-post","status-publish","format-standard","hentry","category-upsc-geoscientist","tag-1105","tag-electric-current","tag-physics","no-featured-image-padding"],"yoast_head":"\nThe $I-V$ graph for two resistors, resistor 1 ($R_1$) and resistor 2 (<\/title>\n<meta name=\"description\" content=\"The correct answer is D) Up to $V_1$, the resistance of $R_1$ is larger than that of $R_2$. The resistance $R$ of a component can be determined from its I-V graph as $R = V\/I$. This is equivalent to $R = 1 \/ (text{slope of the I-V graph})$ if the graph plots I on the y-axis and V on the x-axis, as shown in the image. For resistor $R_1$, the graph is a straight line passing through the origin, indicating that $R_1$ is an ohmic resistor and follows Ohm's law. Its resistance is constant. The slope of the $R_1$ line (I\/V) is constant. For resistor $R_2$, the graph is a curve. Up to voltage $V_1$, the graph is approximately linear but less steep than $R_1$. The slope of the $R_2$ curve (I\/V) is smaller than the slope of the $R_1$ line in this region. Since resistance $R = 1 \/ (text{slope of I-V graph})$, a smaller slope corresponds to a larger resistance. Comparing the slopes up to $V_1$: (Slope of $R_1$) > (Slope of $R_2$). Therefore, (Resistance of $R_1$) < (Resistance of $R_2$). Statement A is correct because $R_1$ graph is a straight line through origin. Statement B is correct because the curve of $R_2$ after $V_1$ shows that its resistance (V\/I or $1\/$slope) changes (increases as V increases). Statement C says "Up to $V_1$, the resistance of $R_1$ is smaller than that of $R_2$". This is consistent with our finding that $R_1 < R_2$ up to $V_1$. So C is correct. Statement D says "Up to $V_1$, the resistance of $R_1$ is larger than that of $R_2$". This contradicts Statement C and our analysis. Therefore, Statement D is not correct.\" \/>\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\/the-i-v-graph-for-two-resistors-resistor-1-r_1-and-resistor-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The $I-V$ graph for two resistors, resistor 1 ($R_1$) and resistor 2 (\" \/>\n<meta property=\"og:description\" content=\"The correct answer is D) Up to $V_1$, the resistance of $R_1$ is larger than that of $R_2$. The resistance $R$ of a component can be determined from its I-V graph as $R = V\/I$. This is equivalent to $R = 1 \/ (text{slope of the I-V graph})$ if the graph plots I on the y-axis and V on the x-axis, as shown in the image. For resistor $R_1$, the graph is a straight line passing through the origin, indicating that $R_1$ is an ohmic resistor and follows Ohm's law. Its resistance is constant. The slope of the $R_1$ line (I\/V) is constant. For resistor $R_2$, the graph is a curve. Up to voltage $V_1$, the graph is approximately linear but less steep than $R_1$. The slope of the $R_2$ curve (I\/V) is smaller than the slope of the $R_1$ line in this region. Since resistance $R = 1 \/ (text{slope of I-V graph})$, a smaller slope corresponds to a larger resistance. Comparing the slopes up to $V_1$: (Slope of $R_1$) > (Slope of $R_2$). Therefore, (Resistance of $R_1$) < (Resistance of $R_2$). Statement A is correct because $R_1$ graph is a straight line through origin. Statement B is correct because the curve of $R_2$ after $V_1$ shows that its resistance (V\/I or $1\/$slope) changes (increases as V increases). Statement C says "Up to $V_1$, the resistance of $R_1$ is smaller than that of $R_2$". This is consistent with our finding that $R_1 < R_2$ up to $V_1$. So C is correct. Statement D says "Up to $V_1$, the resistance of $R_1$ is larger than that of $R_2$". This contradicts Statement C and our analysis. Therefore, Statement D is not correct.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/the-i-v-graph-for-two-resistors-resistor-1-r_1-and-resistor-2\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T04:27:19+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":"The $I-V$ graph for two resistors, resistor 1 ($R_1$) and resistor 2 (","description":"The correct answer is D) Up to $V_1$, the resistance of $R_1$ is larger than that of $R_2$. The resistance $R$ of a component can be determined from its I-V graph as $R = V\/I$. This is equivalent to $R = 1 \/ (text{slope of the I-V graph})$ if the graph plots I on the y-axis and V on the x-axis, as shown in the image. For resistor $R_1$, the graph is a straight line passing through the origin, indicating that $R_1$ is an ohmic resistor and follows Ohm's law. Its resistance is constant. The slope of the $R_1$ line (I\/V) is constant. For resistor $R_2$, the graph is a curve. Up to voltage $V_1$, the graph is approximately linear but less steep than $R_1$. The slope of the $R_2$ curve (I\/V) is smaller than the slope of the $R_1$ line in this region. Since resistance $R = 1 \/ (text{slope of I-V graph})$, a smaller slope corresponds to a larger resistance. Comparing the slopes up to $V_1$: (Slope of $R_1$) > (Slope of $R_2$). Therefore, (Resistance of $R_1$) < (Resistance of $R_2$). Statement A is correct because $R_1$ graph is a straight line through origin. Statement B is correct because the curve of $R_2$ after $V_1$ shows that its resistance (V\/I or $1\/$slope) changes (increases as V increases). Statement C says "Up to $V_1$, the resistance of $R_1$ is smaller than that of $R_2$". This is consistent with our finding that $R_1 < R_2$ up to $V_1$. So C is correct. Statement D says "Up to $V_1$, the resistance of $R_1$ is larger than that of $R_2$". This contradicts Statement C and our analysis. Therefore, Statement D is not correct.","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\/the-i-v-graph-for-two-resistors-resistor-1-r_1-and-resistor-2\/","og_locale":"en_US","og_type":"article","og_title":"The $I-V$ graph for two resistors, resistor 1 ($R_1$) and resistor 2 (","og_description":"The correct answer is D) Up to $V_1$, the resistance of $R_1$ is larger than that of $R_2$. The resistance $R$ of a component can be determined from its I-V graph as $R = V\/I$. This is equivalent to $R = 1 \/ (text{slope of the I-V graph})$ if the graph plots I on the y-axis and V on the x-axis, as shown in the image. For resistor $R_1$, the graph is a straight line passing through the origin, indicating that $R_1$ is an ohmic resistor and follows Ohm's law. Its resistance is constant. The slope of the $R_1$ line (I\/V) is constant. For resistor $R_2$, the graph is a curve. Up to voltage $V_1$, the graph is approximately linear but less steep than $R_1$. The slope of the $R_2$ curve (I\/V) is smaller than the slope of the $R_1$ line in this region. Since resistance $R = 1 \/ (text{slope of I-V graph})$, a smaller slope corresponds to a larger resistance. Comparing the slopes up to $V_1$: (Slope of $R_1$) > (Slope of $R_2$). Therefore, (Resistance of $R_1$) < (Resistance of $R_2$). Statement A is correct because $R_1$ graph is a straight line through origin. Statement B is correct because the curve of $R_2$ after $V_1$ shows that its resistance (V\/I or $1\/$slope) changes (increases as V increases). Statement C says "Up to $V_1$, the resistance of $R_1$ is smaller than that of $R_2$". This is consistent with our finding that $R_1 < R_2$ up to $V_1$. So C is correct. Statement D says "Up to $V_1$, the resistance of $R_1$ is larger than that of $R_2$". This contradicts Statement C and our analysis. Therefore, Statement D is not correct.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/the-i-v-graph-for-two-resistors-resistor-1-r_1-and-resistor-2\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T04:27:19+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\/the-i-v-graph-for-two-resistors-resistor-1-r_1-and-resistor-2\/","url":"https:\/\/exam.pscnotes.com\/mcq\/the-i-v-graph-for-two-resistors-resistor-1-r_1-and-resistor-2\/","name":"The $I-V$ graph for two resistors, resistor 1 ($R_1$) and resistor 2 (","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T04:27:19+00:00","dateModified":"2025-06-01T04:27:19+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The correct answer is D) Up to $V_1$, the resistance of $R_1$ is larger than that of $R_2$. The resistance $R$ of a component can be determined from its I-V graph as $R = V\/I$. This is equivalent to $R = 1 \/ (\\text{slope of the I-V graph})$ if the graph plots I on the y-axis and V on the x-axis, as shown in the image. For resistor $R_1$, the graph is a straight line passing through the origin, indicating that $R_1$ is an ohmic resistor and follows Ohm's law. Its resistance is constant. The slope of the $R_1$ line (I\/V) is constant. For resistor $R_2$, the graph is a curve. Up to voltage $V_1$, the graph is approximately linear but less steep than $R_1$. The slope of the $R_2$ curve (I\/V) is smaller than the slope of the $R_1$ line in this region. Since resistance $R = 1 \/ (\\text{slope of I-V graph})$, a smaller slope corresponds to a larger resistance. Comparing the slopes up to $V_1$: (Slope of $R_1$) > (Slope of $R_2$). Therefore, (Resistance of $R_1$) < (Resistance of $R_2$). Statement A is correct because $R_1$ graph is a straight line through origin. Statement B is correct because the curve of $R_2$ after $V_1$ shows that its resistance (V\/I or $1\/$slope) changes (increases as V increases). Statement C says "Up to $V_1$, the resistance of $R_1$ is smaller than that of $R_2$". This is consistent with our finding that $R_1 < R_2$ up to $V_1$. So C is correct. Statement D says "Up to $V_1$, the resistance of $R_1$ is larger than that of $R_2$". This contradicts Statement C and our analysis. Therefore, Statement D is not correct.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/the-i-v-graph-for-two-resistors-resistor-1-r_1-and-resistor-2\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/the-i-v-graph-for-two-resistors-resistor-1-r_1-and-resistor-2\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-i-v-graph-for-two-resistors-resistor-1-r_1-and-resistor-2\/#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":"The $I-V$ graph for two resistors, resistor 1 ($R_1$) and resistor 2 ("}]},{"@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\/87062","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=87062"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/87062\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=87062"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=87062"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=87062"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}