A 3,^oC rise in temperature is observed in a | vedclass

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(B) The heat produced in a conductor is given by Joule's law of heating: $H = I^2Rt$.This heat causes a rise in temperature $	heta$ in the conductor,

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$12$

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(B) The heat produced in a conductor is given by Joule's law of heating: $H = I^2Rt$.This heat causes a rise in temperature $	heta$ in the conductor,given by $H = C	heta$,where $C$ is the thermal capacity of the conductor.Initially,for current $I$,the rise in temperature is $	heta = 3\,^oC$. Thus,$I^2Rt = C(3)$.When the current is doubled,the new current is $I' = 2I$.The new heat produced is $H' = (I')^2Rt = (2I)^2Rt = 4I^2Rt$.Since $H' = C	heta'$,we have $C	heta' = 4(I^2Rt)$.Substituting $I^2Rt = 3C$ into the equation,we get $C	heta' = 4(3C) = 12C$.Therefore,$	heta' = 12\,^oC$.

$A$ $3\,^oC$ rise in temperature is observed in a conductor by passing a certain current. When the current is doubled,the rise in temperature will be ............. $^oC$.

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