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प्रश्न
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? The temperature coefficient of resistance of nichrome averaged over the temperature range involved is 1.70 × 10−4 °C−1.
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उत्तर
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
T2 can 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.
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