{"id":342673,"date":"2023-01-06T12:57:51","date_gmt":"2023-01-06T07:27:51","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/100-j-of-heat-is-produced-each-second-in-a-4-%cf%89-resistance-which-of-the-following-is-the-potential-difference-across-the-resistor\/"},"modified":"2025-06-26T17:53:05","modified_gmt":"2025-06-26T12:23:05","slug":"100-j-of-heat-is-produced-each-second-in-a-4-%cf%89-resistance-which-of-the-following-is-the-potential-difference-across-the-resistor","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/100j-of-heat-is-produced-each-second-in-a-4-resistance-w\/","title":{"rendered":"100\u00a0J of heat is produced each second in a 4\u00a0\u2126 resistance. Which of the following is the potential difference across the resistor?"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"100\u00a0J of heat is produced each second in a 4\u00a0\u2126 resistance. Which of the following is the potential difference across the resistor?","custom_permalink":"question\/physics\/100j-of-heat-is-produced-each-second-in-a-4-resistance-w\/"},"categories":[],"acf":{"question":"<p style=\"margin-top:0pt; margin-bottom:8pt; line-height:107%; font-size:12pt\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>100<\/mn><mi mathvariant=\"italic\">&nbsp;J<\/mi><\/math><span> of heat is produced each second in a <\/span><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>4<\/mn><mi mathvariant=\"italic\">&nbsp;\u2126<\/mi><\/math><span> resistance. Which of the following is the potential difference across the resistor?<\/span><\/p><br><pstyle=\"margin-top:0pt;margin-bottom:8pt;line-height:107%;font-size:12pt\"><spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><p><\/p><spanstyle=\"font-family:'timesnewroman';-aw-import:spaces\"><pstyle=\"margin-top:0pt;margin-bottom:8pt;line-height:107%;font-size:12pt\"><spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><p><\/p><\/spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:8pt;line-height:107%;font-size:12pt\"><\/spanstyle=\"font-family:'timesnewroman';-aw-import:spaces\"><\/spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:8pt;line-height:107%;font-size:12pt\">","options":[{"option":"<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>20<\/mn><mi mathvariant=\"italic\">&nbsp;V<\/mi><\/math><span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <\/span>","correct":true},{"option":"<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>40<\/mn><mi mathvariant=\"italic\">&nbsp;V<\/mi><\/math><span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <\/span>","correct":false},{"option":"<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>50<\/mn><mi mathvariant=\"italic\">&nbsp;V<\/mi><\/math><span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <\/span>","correct":false},{"option":"None of these<span>&nbsp;<\/span>","correct":false}],"solution":"<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>100<\/mn><mi mathvariant=\"italic\">&nbsp;J<\/mi><\/math><span> of heat is produced each second in a <\/span><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>4<\/mn><mi mathvariant=\"italic\">&nbsp;\u2126<\/mi><\/math><span> resistance. The potential difference across the resistor is <\/span><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>20<\/mn><mi mathvariant=\"italic\">&nbsp;V<\/mi><\/math><span>.<\/span><br><span>Given,<\/span><span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <\/span><span>Resistance, <\/span><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>R<\/mi><mo>=<\/mo><mi>&nbsp;<\/mi><mn>4<\/mn><mi mathvariant=\"italic\">&nbsp;\u2126<\/mi><\/math><br><span>Taking time<\/span><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>,<\/mo><mi mathvariant=\"italic\">&nbsp;t<\/mi><mo>=<\/mo><mi>&nbsp;<\/mi><mn>1<\/mn><mi mathvariant=\"italic\">&nbsp;s&nbsp;<\/mi><\/math><br><span>heat produced, <\/span><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>H<\/mi><mo>=<\/mo><mi>&nbsp;<\/mi><mn>100<\/mn><mi mathvariant=\"italic\">&nbsp;J<\/mi><\/math><span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <\/span><span>We know that,<\/span><span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <\/span><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>H<\/mi><mo>=<\/mo><mfrac><mrow><msup><mrow><mi>V<\/mi><\/mrow><mrow><mn>2<\/mn><\/mrow><\/msup><\/mrow><mrow><mi>R<\/mi><\/mrow><\/mfrac><mi>t<\/mi><\/math><span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <\/span><span>Therefore, potential difference across the resistor, <\/span><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>V<\/mi><mo>=<\/mo><msqrt><mrow><mfrac><mrow><mi mathvariant=\"italic\">HR<\/mi><\/mrow><mrow><mi>t<\/mi><\/mrow><\/mfrac><\/mrow><\/msqrt><\/math><span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <\/span><span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <\/span><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><msqrt><mrow><mfrac><mrow><mn>100<\/mn><mo>\u00d7<\/mo><mn>4<\/mn><\/mrow><mrow><mn>1<\/mn><\/mrow><\/mfrac><\/mrow><\/msqrt><\/math><br><span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <\/span><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>=<\/mo><mi>&nbsp;<\/mi><mn>20<\/mn><mi mathvariant=\"italic\">&nbsp;V<\/mi><\/math><br><span>&nbsp;<\/span>","subject":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>100\u00a0J of heat is produced each second in a 4\u00a0\u2126 resistance. 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