Question

A heating element using nichrome connected to a 230 V supplydraws 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 heatingelement if the room temperature is 27.0 °C? Temperature coefficientof resistance of nichrome averaged over the temperature rangeinvolved is 1.70 × 10–4 °C–1.

Answer 1

Given: The initial current drawn is 3.2 A, the supply voltage is 230 V, the steady state value of the current is 2.8 A, the room temperature is 27°C and the temperature coefficient is 1.70× 10 −4  ° C −1 .

The initial resistance is given as,

R 1 = V I 1

Where, the supply voltage is V, the initial current drawn is I 1 and the resistance is R 1 .

By substituting the given values in the above equation, we get

R 1 = 230 3.2 =71.87 Ω

The resistance at steady state is given as,

R 2 = V I 2

Where, the supply voltage is V, the current at steady state is I 2 and the resistance at steady state is R 2 .

By substituting the given values in the above formula, we get

R 2 = 230 2.8 =82.14 Ω

The temperature coefficient is given as,

α= R 2 − R 1 R 1 ( T 2 − T 1 )

Where, the steady state temperature is T 2 , the room temperature is T 1 and the temperature coefficient is α.

By substituting the given values in the above formula, we get

1.7× 10 −4 = 82.14−71.87 71.87×( T 2 −27°C ) T 2 =840.5+27 =867.5 °C

Thus, the steady state temperature of the heating element is 867.5°C.