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.

Answer :

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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