A heating element using nichrome connected to a 115 V supply draws a current of 1.6A which settles after a few seconds to a steady value of 1.4 A. What is the steady temperature of the heating element if the room temperature is `30^@C` ? Temperature coefficient of resistance of nichrome averaged over the temperature range involved is `1.7xx10^(-4).^(@)C^(-1)`.

Explanation

Here, initial room temperature,
`t_(1)=30^@C, I_(1) =1.6 A, V=115 V, alpha =1.7xx10^(-4).^(@)C^(-1)`
Let `t_(2)^@C` be the final steady temperature when current settles down to, `I_(2)=1.4A`.
Initial resistance, `R_(t_1) = V/I_(1)=115/1.6=71.875 Omega`,
final resistance, `R_(t_2) = V/I_(2)=115/1.4=82.143 Omega`,
`alpha=1.7 xx 10^(-4).^(@)C^(-1)`
As, `t_(2)-t_(1)=(R_(t_2) - R_(t_1))/(R_(t_1) xx alpha)`
`:. t-30 =(R_(t_2) - R_(t_1))/(R_(t_1) alpha)=(82.143 - 71.875)/(71.875 xx 1.7 xx10^(-4))`
`=840.3^@C`
Hence, `t=840.3+30=870.3^@C`