{"id":343926,"date":"2023-01-06T13:41:30","date_gmt":"2023-01-06T08:11:30","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/a-coil-in-the-heater-consumes-power-p-on-passing-current-if-it-is-cut-into-halves-and-joined-in-parallel-will-it-consume-power\/"},"modified":"2025-06-26T17:55:11","modified_gmt":"2025-06-26T12:25:11","slug":"a-coil-in-the-heater-consumes-power-p-on-passing-current-if-it-is-cut-into-halves-and-joined-in-parallel-will-it-consume-power","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-coil-in-the-heater-consumes-power-p-on-passing-current-if\/","title":{"rendered":"A coil in the heater consumes power P on passing current. If it is cut into halves and joined in parallel, will it consume power?"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"A coil in the heater consumes power P on passing current. If it is cut into halves and joined in parallel, will it consume power?","custom_permalink":"question\/physics\/a-coil-in-the-heater-consumes-power-p-on-passing-current-if\/"},"categories":[],"acf":{"question":"

A coil in the heater consumes power <\/span>P<\/mi><\/math> on passing current. If it is cut into halves and joined in parallel, will it consume power?<\/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":[{"option":"P<\/mi><\/math>","correct":false},{"option":"P<\/mi><\/mrow>2<\/mn><\/mrow><\/mfrac><\/math>","correct":false},{"option":"2<\/mn>P<\/mi><\/math>","correct":false},{"option":"4<\/mn>P<\/mi><\/math> <\/span>","correct":true}],"solution":"A coil in the heater consumes power <\/span>P<\/mi><\/math> on passing current. If it is cut into halves and joined in parallel, will it consume power is <\/span>4<\/mn>P<\/mi><\/math>.<\/span>
It is given that the coil is cut into two pieces and hence the resistance of each piece turn out to be<\/span> <\/mi>R<\/mi><\/mrow>2<\/mn><\/mrow><\/mfrac><\/math>.<\/span>
The equivalent resistance of the parallel connection is given by,<\/span>
1<\/mn><\/mrow>R<\/mi><\/mrow>P<\/mi><\/mrow><\/msub><\/mrow><\/mfrac>=<\/mo>1<\/mn><\/mrow>R<\/mi><\/mrow>1<\/mn><\/mrow><\/msub><\/mrow><\/mfrac>+<\/mo>1<\/mn><\/mrow>R<\/mi><\/mrow>2<\/mn><\/mrow><\/msub><\/mrow><\/mfrac><\/math>
<\/a>\u21d2<\/mo>1<\/mn><\/mrow>R<\/mi><\/mrow>P<\/mi><\/mrow><\/msub><\/mrow><\/mfrac>=<\/mo>1<\/mn><\/mrow>R<\/mi><\/mrow>2<\/mn><\/mrow><\/mfrac><\/mrow><\/mfrac>+<\/mo>1<\/mn><\/mrow>R<\/mi><\/mrow>2<\/mn><\/mrow><\/mfrac><\/mrow><\/mfrac><\/math>
\u21d2<\/mo>1<\/mn><\/mrow>R<\/mi><\/mrow>P<\/mi><\/mrow><\/msub><\/mrow><\/mfrac>=<\/mo>2<\/mn><\/mrow>R<\/mi><\/mrow><\/mfrac>+<\/mo>2<\/mn><\/mrow>R<\/mi><\/mrow><\/mfrac><\/math>
\u21d2<\/mo>1<\/mn><\/mrow>R<\/mi><\/mrow>P<\/mi><\/mrow><\/msub><\/mrow><\/mfrac>=<\/mo>4<\/mn><\/mrow>R<\/mi><\/mrow><\/mfrac><\/math>
\u21d2<\/mo>R<\/mi><\/mrow>P<\/mi><\/mrow><\/msub>=<\/mo>R<\/mi><\/mrow>4<\/mn><\/mrow><\/mfrac><\/math>
Therefore, new power consumed when two halves of wire are joined in parallel connection is equal to,<\/span>
P<\/mi><\/mrow>'<\/mo><\/mrow><\/msup>=<\/mo>V\u00b2<\/mi><\/mrow>R<\/mi><\/mrow>P<\/mi><\/mrow><\/msub><\/mrow><\/mfrac><\/math>
\u21d2<\/mo>P<\/mi><\/mrow>'<\/mo><\/mrow><\/msup>=<\/mo>V\u00b2<\/mi><\/mrow>R<\/mi><\/mrow>4<\/mn><\/mrow><\/mfrac><\/mrow><\/mfrac><\/math>
\u21d2<\/mo>P<\/mi><\/mrow>'<\/mo><\/mrow><\/msup>=<\/mo>4<\/mn>V\u00b2<\/mi><\/mrow>R<\/mi><\/mrow><\/mfrac><\/math>
\u21d2<\/mo>P<\/mi><\/mrow>'<\/mo><\/mrow><\/msup>=<\/mo>4<\/mn>P<\/mi><\/math>
Hence, the new power is four times the old power when the wire is cut into two halves and joined parallelly.<\/span>
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