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(D) The heat produced in a conductor due to the flow of current is given by Joule's law of heating: $H = I^2Rt$.This heat energy causes a rise in temp

Vedclass · Accepted Answer

$36$

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(D) The heat produced in a conductor due to the flow of current is given by Joule's law of heating: $H = I^2Rt$.This heat energy causes a rise in temperature,given by $H = ms\Delta	heta$,where $m$ is mass,$s$ is specific heat capacity,and $\Delta	heta$ is the temperature rise.Equating the two,we get: $I^2Rt = ms\Delta	heta$. Assuming $R$,$t$,$m$,and $s$ remain constant,we have $\Delta	heta \propto I^2$.Initially,for current $I$,the temperature rise is $\Delta	heta_1 = 4\,^oC$.When the current is tripled,$I' = 3I$. The new temperature rise $\Delta	heta_2$ is given by $\frac{\Delta	heta_2}{\Delta	heta_1} = \frac{(I')^2}{I^2} = \frac{(3I)^2}{I^2} = 9$.Therefore,$\Delta	heta_2 = 9 	imes \Delta	heta_1 = 9 	imes 4\,^oC = 36\,^oC$.

$A$ rise of temperature of $4\,^oC$ is observed in a conductor by passing a current. If the current is tripled,the rise in temperature will be .............. $^oC$.

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