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(C) When the current through the element is very small,heating effects can be ignored and the temperature $T_{1}$ of the element is the same as room t

Vedclass · Accepted Answer

$847$

Vedclass · Answer

(C) When the current through the element is very small,heating effects can be ignored and the temperature $T_{1}$ of the element is the same as room temperature.When the toaster is connected to the supply,its initial current will be slightly higher than its steady value of $2.68\; A$. But due to the heating effect of the current,the temperature will rise. This will cause an increase in resistance and a slight decrease in current.In a few seconds,a steady state will be reached when the temperature will rise no further,and both the resistance of the element and the current drawn will achieve steady values.The resistance $R_{2}$ at the steady temperature $T_{2}$ is:$R_{2} = \frac{230\; V}{2.68\; A} = 85.8\; \Omega$Using the relation:$R_{2} = R_{1}[1 + \alpha(T_{2} - T_{1})]$With $\alpha = 1.70 	imes 10^{-4}\; ^{\circ} C^{-1}$,we get:$T_{2} - T_{1} = \frac{(85.8 - 75.3)}{(75.3) 	imes 1.70 	imes 10^{-4}} = 820^{\circ} C$That is,$T_{2} = (820 + 27.0)^{\circ} C = 847^{\circ} C$.Thus,the steady temperature of the heating element is $847^{\circ} C$.

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