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Question:

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 x 10-4 °C -1.

Answer:

Supply voltage, V = 230 V

Initial current drawn, I1 = 3.2 A

Initial resistance = R1, which is given by the relation,

Steady state value of the current, I2 = 2.8 A

Resistance at the steady state = R2, which is given as

Temperature co-efficient of nichrome, α = 1.70 × 10 - 4 °C - 1

Initial temperature of nichrome, T1= 27.0°C

Study state temperature reached by nichrome = T2  

T2 can be obtained by the relation for α,

Therefore, the steady temperature of the heating element is 867.5°C


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