Ncert Exercises & Solutions

3.8 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.

Supply voltage, V = 230 V

Initial current drawn, I1 = 3.2 A

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

$R_{1} = \frac{V}{I} = \frac{230}{3.2} = 71.87 Ω$

Steady state value of the current, I2 = 2.8 A

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

$R_{2} = \frac{230}{2.8} = 82.14 Ω$

Temperature co-efficient of nichrome, $α = 1.70 \times 10^{- 4} ° C^{- 1}$

Initial temperature of nichrome, T1 = $27.0 ° C$

Study state temperature reached by nichrome = T2

T2 can be obtained by the relation for $α$ ,

$α = \frac{R_{2} - R_{1}}{R_{1} (T_{2} - T_{1})}$
$T_{2} - 27 ° C = \frac{82.14 - 71.87}{71.87 \times 1.7 \times 10^{- 4}} = 840.5$
$T_{2} = 840.5 + 27 = 867.5 ° C$

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

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