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. - Physics

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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.

Solution

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 × 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,

α = ("R"_2 - "R"_1)/("R"_1("T"_2 - "T"_1))

T2 − 27°C = (82.14 - 71.87)/(71.87 xx 1.7 xx 10^-4) = 840.5

T2 = 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 Physics Part 1 and 2 Class 12
Chapter 3 Current Electricity
Exercise | Q 3.8 | Page 127
NCERT Class 12 Physics Textbook
Chapter 3 Current Electricity
Exercise | Q 8 | Page 127
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