Question

A heating element using nichrome connected to a 230 V supply draws 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 heating element if the room temperature is `27^(@)C` ? Temperature coefficient of resistance of nichrome averaged over the temperature range involved is `(1.70xx10^(-4))^@ C^(-1)`.

Answer 1

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) = 71.87 Omega`
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) = 82.14 Omega`
Temperature co-efficient of nichrome, `a= 1.70 xx 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 a,
`alpha = (R_(2)- R_(1))/(R_(1)(T_(2)-T_(1)))`
`T_(2) = 27^(@)C = (82.14 - 71.87)/(71.87 xx1.7 xx 10^(-4))=840.5`
`T_(2) = 840.5 +27 = 867.5^(@)C`
Therefore, the steady temperature of the heating element is `867.5^(@)C`.