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A heating element using nichrome connected to a 230 V supply draws an initial current of 3.2 Awhich settles after a few seconds to a steady value of 2.8 A. What is the steady temperature of the heating element if the room temperature is 27.0^@C? Temperature coefficient of resistanceof nichrome averaged over the temperature range involved is 1.70 xx 10^(-4) ""^@C^(-1) . |
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Answer» Solution :Here V = 230 V and at `T_1 = 27^@C` , current `I_1 = 3.2 A` ` therefore R_1 = (V)/(I_1) = (230)/(3.2) Omega` Again at a steady temperature `T_2` of the heating ELEMENT , current `I_2 = 2.8A` `therefore R_2 = (V)/(I_2) = (230)/(2.8) Omega` Moreover temperature coefficient of resistance `alpha = 1.70 XX 10^(-4) ""^@C^(-1)` using the relation `R_2 = R_1 [1+ alpha (T_2 - T_1) ]` , we have `T_2 -T_1 = (R_2 - R_1)/(R_1- alpha) = ( (230)/(2.8) - (230)/(3.2) )/( (230)/(3.2) xx 1.7 xx 10^(-4) ) = 840` `T_2 = T_1 + 840 = 27 + 840 = 867^@C` |
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