{"id":346583,"date":"2023-01-06T15:18:26","date_gmt":"2023-01-06T09:48:26","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/a-student-boils-the-water-in-an-electric-kettle-for-20-minutes-after-being-switched-on-if-the-boiling-time-is-to-be-decreased-then-the-length-of-the-heating-element-should-be-1\/"},"modified":"2025-06-26T18:22:11","modified_gmt":"2025-06-26T12:52:11","slug":"a-student-boils-the-water-in-an-electric-kettle-for-20-minutes-after-being-switched-on-if-the-boiling-time-is-to-be-decreased-then-the-length-of-the-heating-element-should-be-1","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-student-boils-the-water-in-an-electric-kettle-for-20minut\/","title":{"rendered":"A student boils the water in an electric kettle for 20\u00a0minutes after being switched on. If the boiling time is to be decreased then the length of the heating element should be [[1]]."},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"A student boils the water in an electric kettle for 20\u00a0minutes after being switched on. If the boiling time is to be decreased then the length of the heating element should be [[1]].","custom_permalink":"question\/physics\/a-student-boils-the-water-in-an-electric-kettle-for-20minut\/"},"categories":[],"acf":{"question":"

A student boils the water in an electric kettle for <\/span>20<\/mn> <\/mi>minutes<\/mi><\/math> after being switched on. If the boiling time is to be decreased then the length of the heating element should be [[1]].<\/span><\/p>

<\/p>

<\/p><\/spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:115%;font-size:12pt\"><\/spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:115%;font-size:12pt\">","options":null,"solution":"The student should decrease the length of the heating element to decrease the boiling time.<\/span>
By Ohm\u2019s law of heating, the heat produced is given as<\/span>
     <\/span>H<\/mi>=<\/mo>I<\/mi><\/mrow>2<\/mn><\/mrow><\/msup>Rt<\/mi><\/math>, <\/span>
But it is known that the current is given as <\/span>
     <\/span>I<\/mi> <\/mi>=<\/mo> <\/mi>V<\/mi>\/<\/mo>R<\/mi><\/math>  <\/span>Hence the equation for the heat produced can also be written as<\/span>
   <\/span>H<\/mi> <\/mi>=<\/mo> <\/mi>V<\/mi><\/mrow>2<\/mn><\/mrow><\/msup>t<\/mi><\/mrow>R<\/mi><\/mrow><\/mfrac><\/math>
Since, the heat required is the same in both cases, it can be stated that<\/span>
V<\/mi><\/mrow>2<\/mn><\/mrow><\/msup>t<\/mi><\/mrow>1<\/mn><\/mrow><\/msub><\/mrow>R<\/mi><\/mrow>1<\/mn><\/mrow><\/msub><\/mrow><\/mfrac>=<\/mo>V<\/mi><\/mrow>2<\/mn><\/mrow><\/msup>t<\/mi><\/mrow>2<\/mn><\/mrow><\/msub><\/mrow>R<\/mi><\/mrow>2<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><\/math> or it can be written as<\/span>
  <\/span>t<\/mi><\/mrow>1<\/mn><\/mrow><\/msub><\/mrow>t<\/mi><\/mrow>2<\/mn><\/mrow><\/msub><\/mrow><\/mfrac>=<\/mo>R<\/mi><\/mrow>1<\/mn><\/mrow><\/msub><\/mrow>R<\/mi><\/mrow>2<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><\/math> <\/span>From the above relation, for t<\/span>2 <\/span>to be less than t<\/span>1<\/span>, R<\/span>2 <\/span>should be lesser than R<\/span>1<\/span> if we want the water to boil quicker.<\/span>
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