{"id":259153,"date":"2022-09-10T12:11:33","date_gmt":"2022-09-10T06:41:33","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/ten-identical-cells-connected-in-series-are-needed-to-heat-a-wire-of-length-one-meter-and-radius-r-by-10oc-in-time-t-how-many-cells-will-be-required-to-h\/"},"modified":"2022-09-10T12:11:33","modified_gmt":"2022-09-10T06:41:33","slug":"ten-identical-cells-connected-in-series-are-needed-to-heat-a-wire-of-length-one-meter-and-radius-r-by-10oc-in-time-t-how-many-cells-will-be-required-to-h","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/ten-identical-cells-connected-in-series-are-needed-to-heat-a\/","title":{"rendered":"Ten identical cells connected in series are needed to heat a wire of length one meter and radius \u2018r\u2019 by\u00a010oC\u00a0in time \u2018t\u2019. How many cells will be required to heat the wire of length two meter of the same radius by the same temperature in time \u2018t\u2019 ?"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Ten identical cells connected in series are needed to heat a wire of length one meter and radius \u2018r\u2019 by\u00a010oC\u00a0in time \u2018t\u2019. How many cells will be required to heat the wire of length two meter of the same radius by the same temperature in time \u2018t\u2019 ?","custom_permalink":"question\/physics\/ten-identical-cells-connected-in-series-are-needed-to-heat-a\/"},"categories":[],"acf":{"question":"

Ten identical cells connected in series are needed to heat a wire of length one meter and radius \u2018r\u2019 by 10<\/mn>o<\/mi><\/msup>C<\/mi><\/math> in time \u2018t\u2019. How many cells will be required to heat the wire of length two meter of the same radius by the same temperature in time \u2018t\u2019 ?<\/p>","options":[{"option":"

20<\/p>","correct":true},{"option":"

30<\/p>","correct":false},{"option":"

40<\/p>","correct":false},{"option":"

10<\/p>","correct":false}],"solution":"

Let \u03c1<\/mi><\/math> be resistivity of the material of the wire and r be radius of the wire. Therefore, resistance of 1 m wire is<\/p>

R<\/mi>=<\/mo>\u03c1<\/mi>(<\/mo>1<\/mn>)<\/mo><\/mrow>\u03c0<\/mi>r<\/mi>2<\/mn><\/msup><\/mrow><\/mfrac>=<\/mo>\u03c1<\/mi>\u03c0<\/mi>r<\/mi>2<\/mn><\/msup><\/mrow><\/mfrac>  <\/mo>\u2235<\/mo>R<\/mi>=<\/mo>\u03c1<\/mi>l<\/mi><\/mrow>A<\/mi><\/mfrac><\/mrow><\/mfenced><\/math><\/p>

Let \u03b5<\/mi><\/math> be emf of each cell. <\/p>

In first case,<\/p>

<\/figure>

10 cells each of emf \u03b5<\/mi><\/math> are connected in series to heat the wire of length 1 m by \u0394<\/mi>T<\/mi>(<\/mo>=<\/mo>10<\/mn>o<\/mi><\/msup>C<\/mi>)<\/mo><\/math>in time t.<\/p>

\u2234<\/mo>  <\/mo>(<\/mo>10<\/mn>\u03b5<\/mi>)<\/mo>2<\/mn><\/msup><\/mrow>R<\/mi><\/mfrac>t<\/mi>=<\/mo>m<\/mi>s<\/mi>\u0394<\/mi>T<\/mi> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo>.<\/mo>.<\/mo>.<\/mo>.<\/mo>.<\/mo>.<\/mo>.<\/mo>.<\/mo>(<\/mo>i<\/mi>)<\/mo><\/math><\/p>

In second case, Resistance of same wire of length 2 m is<\/p>

R<\/mi>'<\/mo><\/msup>=<\/mo>\u03c1<\/mi>(<\/mo>2<\/mn>)<\/mo><\/mrow>\u03c0<\/mi>r<\/mi>2<\/mn><\/msup><\/mrow><\/mfrac>=<\/mo>2<\/mn>\u03c1<\/mi><\/mrow>\u03c0<\/mi>r<\/mi>2<\/mn><\/msup><\/mrow><\/mfrac>=<\/mo>2<\/mn>R<\/mi><\/math><\/p>
<\/figure>

Let n cells each of emt \u03b5<\/mi><\/math> are connected in series to heat the same wire of length 2 m, in the same temperature \u0394<\/mi>T<\/mi>(<\/mo>=<\/mo>10<\/mn>o<\/mi><\/msup>C<\/mi>)<\/mo><\/math> in the same time t<\/p>

\u2234<\/mo>  <\/mo>(<\/mo>n<\/mi>\u03b5<\/mi>)<\/mo>2<\/mn><\/msup>t<\/mi><\/mrow>2<\/mn>R<\/mi><\/mrow><\/mfrac>=<\/mo>(<\/mo>2<\/mn>m<\/mi>)<\/mo>s<\/mi>\u0394<\/mi>T<\/mi><\/mrow><\/msub> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo> <\/mo>.<\/mo>.<\/mo>.<\/mo>.<\/mo>.<\/mo>(<\/mo>i<\/mi>i<\/mi>)<\/mo><\/math><\/p>

Divide (ii) by (i), we get<\/p>

n<\/mi>2<\/mn><\/msup>200<\/mn><\/mfrac>=<\/mo>2<\/mn>\u21d2<\/mo>n<\/mi>2<\/mn><\/msup>=<\/mo>400<\/mn>\u2234<\/mo>  <\/mo>n<\/mi>=<\/mo>20<\/mn><\/math><\/p>","subject":""},"yoast_head":"\nTen identical cells connected in series are needed to heat a wire of length one meter and radius \u2018r\u2019 by\u00a010oC\u00a0in time \u2018t\u2019. How many cells will be required to heat the wire of length two meter of the same radius by the same temperature in time \u2018t\u2019 ? - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Ten identical cells connected in series are needed to heat a wire of length one meter and radius \u2018r\u2019 by\u00a010oC\u00a0in time \u2018t\u2019. 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