Class 12 Physics
CBSE and UP Board
Current Electricity
Exercise 3
Chapter-3 Exercise 3.8
NCERT Solutions for Class 12 Physics Chapter 3
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 27.0 °C? Temperature coefficient of resistance of nichrome averaged over the temperature range involved is 1.70 × 10⁻⁴ °C⁻¹
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Supply voltage, V = 230 V
Initial current drawn, I₁ = 3.2 A
Initial resistance = R₁, which is given by the relation,
R₁=V/I =230 /3.2 =71.87 Ω
Steady state value of the current, I2 = 2.8 A
Resistance at the steady state = R2, which is given as
R2=230/2.8 = 82.14 Ω
Temperature co-efficient of nichrome,α = 1.70 x 10⁻4 oC⁻1
Initial temperature of nichrome, T₁= 27.0°C
Study state temperature reached by nichrome = T2
T2can be obtained by the relation for α,
α =(R2-R₁)/R ₁(T2-T₁)
(T2-T₁) =(R2-R₁)/α
=> T2-27 = (82.14-71.87 ) /(71.87 x 1.7 x 10⁻4) = 840.5
=> T2 =840.5 + 27 =867.5 °C
Therefore, the steady temperature of the heating element is 867.5°C