3.8 A heating element using nichrome connected to a 230 V supply draws an initial current of 3.2 A which 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 resistance of nichrome averaged over the temperature range involved is 1.70\times 10^{-4}\;\degree C^{-1}.

Answers (1)

For the given voltage, the two values of current will correspond to two different values of resistance which will correspond to two different temperature.

Given,

Voltage, V = 230 V

I_1= 3.2 A  and I_2 = 2.8 A

Using Ohm's law:

R_1 = 230/3.2 = 71.87\Omega  

and

 R_2= 230/2.8 = 82.14 \Omega 

Now, the temperature coefficient of filament,

\alpha = 1.70\times 10^{-4}\degree C^{-1} 

T_1= 27\degree C 

Let T_2 be the steady temperature of the heating element.

We know,

R_2 = R_1[1 + \alpha \Delta T]

\implies 230/2.8 = 230/3.2[1 + (1.70\times 10^{-4}) ( T2 -  27) ]

\implies 3.2/2.8 = 1 + (1.70\times 10^{-4}) ( T2 -  27)

\implies 1.14 - 1 =  (1.70\times 10^{-4}) ( T2 -  27)

\implies T2 -  27 = 0.14 / (1.70\times 10^{-4})

\implies T2  = (840.5 + 27) °C

Hence, Steady temperature of the element is 867.5 °C.

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