# Aheating 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. - Physics

Aheating element using nichrome connected to a 230 V supply draws an initial current of 3.2 A which settles after a few seconds toa 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.

#### Solution

Supply voltage, V = 230 V

Initial current drawn, I1 = 3.2 A

Initial resistance = R1, which is given by the relation,

R_1=V/I

=230/3.2=71.87Omega

Steady state value of the current, I2 = 2.8 A

Resistance at the steady state = R2, which is given as

R_2=230/2.8=82.14Omega

Temperature co-efficient of nichrome, α = 1.70 × 10−4 °C −1

Initial temperature of nichrome, T1= 27.0°C

Study state temperature reached by nichrome = T2

Tcan be obtained by the relation for α,

alpha=(R_2-R_1)/(R_1(T_2-T_1))

T_2-27^@ C=(82.14-71.87)/(71.87xx1.7xx10^-4)=840.5

T_2=840.5+27=867.5^@ C

Therefore, the steady temperature of the heating element is 867.5°C

Concept: Temperature Dependence of Resistance
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#### APPEARS IN

NCERT Class 12 Physics Textbook
Chapter 3 Current Electricity
Q 8 | Page 127