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 co-efficient of resistance of nichrome averaged over the temperature range involved is 1.70 x10^–4 °C^–1.

Solution

Here,
Potential applied across the heating element, V= 230 V
Initial current, I₁ = 3.2 A
After few seconds, steady current attained is, I₂ = 2.8 A

Using ohm's law,

$R_{1} = \frac{230}{3.2} = 71.87 Ω$
and,
$R_{2} = \frac{230}{2.8} = 82.14 Ω α = 1.7 \times 10^{- 4} ° C^{- 1}$

$t_{1} = 27 °$

Using the relation,

$R_{2} = R_{1} [1 + α (t_{2} - t_{1})]$

Therefore, $t_{2} = \frac{R_{2} - R_{1}}{R_{1} . α} + t_{1}$

$\Rightarrow$ $t_{2} = \frac{82.14 - 71.87}{71.87 \times 1.7 \times 10^{- 4}} + 27$

$= 840.56 + 27 = 867.56 ° C = 867 ° C .$

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