Aheating element using nichrome connected to a 230 V supply draws an initial current of 3.2 A which settles after a few seconds toa 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 × 10^{−4 }°C ^{−1}.

#### Solution

Supply voltage,* V* = 230 V

Initial current drawn, *I*_{1} = 3.2 A

Initial resistance = *R*_{1}, which is given by the relation,

`R_1=V/I`

`=230/3.2=71.87Omega`

Steady state value of the current, *I*_{2} = 2.8 A

Resistance at the steady state = *R*_{2}, which is given as

`R_2=230/2.8=82.14Omega`

Temperature co-efficient of nichrome, *α* = 1.70 × 10^{−4 }°C ^{−1}

Initial temperature of nichrome, *T*_{1}= 27.0°C

Study state temperature reached by nichrome = *T*_{2}

*T*_{2 }can be obtained by the relation for *α*,

`alpha=(R_2-R_1)/(R_1(T_2-T_1))`

`T_2-27^@ C=(82.14-71.87)/(71.87xx1.7xx10^-4)=840.5`

`T_2=840.5+27=867.5^@ C`

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