# 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 .

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

and

Using Ohm's law:

and

Now, the temperature coefficient of filament,

=

Let  be the steady temperature of the heating element.

We know,

230/2.8 = 230/3.2[1 + () ( T2 -  27) ]

3.2/2.8 = 1 + () ( T2 -  27)

1.14 - 1 =  () ( T2 -  27)

T2 -  27 = 0.14 / ()

T2  = (840.5 + 27) °C

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

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