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An electric toaster uses nichrome for its heating element. When a negligibly small current passes through it, its resistance at room temperature (27.0^(@)C) is found to be 75.3 Omega . When the toaster is connected to a 230 V supply, the current settles, after a few seconds, to a steady value of 2.68 A. Whatis the steady temperature of the nichrome element ? The temperature coefficient of resistance of nichrome averaged over the temperature range involved , is 1.70 xx 10^(-4) ""^(@) C^(-1). |
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Answer» Solution :Initially when extremely small current PASSES through nichrome filament, its temperature can be taken equal to room temperature `T_(1) = 27^(@) `C. At this temperature its resistance is `R_(1) = 75.3 Omega. ` Now when given toaster is connected across V = 230 volt steady current passing through it (after very SHORT TIME) is I = 2.68 A and its temperature increases to `T_(2)`, which is to be found out. At this temperature resistance of nichrome filament is given by formula `R_(2) = R_(1) { 1 + alpha (T_(2) - T_(1))} ` ( where `alpha ` = temperature coeffeicient of resistance ) `therefore (V)/(I) = R { 1 + alpha (T_(2)- T_(1) ) } ` (` because R_(2) = (V)/(I) `= resistance of hot filament ) `therefore (230)/(2.68)= 75.3{ 1 + 1.7 xx 10^(-4) (T_(2) - 27)} ` `therefore 1.1397 = 1 + 1.7 xx 10^(-4) (T_(2)- 27)` `therefore T_(2) - 27 = (0.1397)/(1.7 xx 10^(-4))` `therefore T_(2) - 27 = 821.76` `therefore = 848.76^(@)` C |
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