Q. 84.1( 35 Votes )
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 due to a 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.
Given Supply Voltage = 230 Volt
And it draws current I1 = 3.2 Ampere
Resistance is given by R1 = V/I
R1 = 230V/3.2A
R1 = 71.87 Ω
Steady value of current I2 = 2.8Ampere
Resistance R α is given by R2 = 230V/2.8A
R2 = 82.14 Ω
Temperature coefficient of nichrome wire α = 1.70 × 10-4 per °C
Initial temperature of nichrome T1 = 27 ° C
Steady Temperature attained by nichrome = T2
The formula is: R2 = R1[1 + α(T2-T1)]
⇒ R2 - R1 = R1α(T2 - T1)
⇒ R2 - R1 = R1α (T2 - T1)
⇒ T2-27°C = 840.5°C
⇒ T2 = 840.5°C + 27°C = 867.5° C
Hence Steady Temperature attained by nichrome = 867.5 ° C.
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