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, I1 = 3.2 A
Initial resistance = R1, which is given by the relation,
`R_1=V/I`
`=230/3.2=71.87Omega`
Steady state value of the current, I2 = 2.8 A
Resistance at the steady state = R2, 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, T1= 27.0°C
Study state temperature reached by nichrome = T2
T2 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
