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 heatinf element it 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

Using Ohm.s law V= IR and temperature dependence of resistance `R_(t) = R_(0) (1 + alpha t)`:
Resistance of element at `30^(@)C R_(1) = (220)/(2.2) =100Omega`
`rArr 100= R_(0) (1 + 1.7 xx 10^(-4) xx 30)` ..(i)
Resistance of element at steady temperature `R_(2) = (220)/(2) = 100Omega`
`rArr 110 R_(0) (1 + 1.7 xx 10^(-4) xx t)` ...(ii)
Dividing equation (ii) by equation (i)
`rArr (110)/(100) = ((1+ 1.7xx 10^(-4) xx t))/((1 + 1.7 xx 10^(-4) xx 30)) rArr t = 620^(@)C`