A heating element using nichrome connected to a 230 V supply draws ...

Question

A heating element using nichrome connected to a 230 V supply draws initial current of 3.2 A which settles to 2.8 A. Find steady temperature if room temperature is 27°C. ($\alpha_{nichrome} = 1.70 	imes 10^{-4}$ °C$^{-1}$)

Accepted Answer

Initial resistance at 27°C: $R_0 = 230/3.2 = 71.875\ \Omega$

Steady resistance: $R = 230/2.8 = 82.14\ \Omega$

Using $R = R_0(1 + \alpha \Delta T)$:

$$82.14 = 71.875(1 + 1.70 \times 10^{-4} \times \Delta T)$$

$$\Delta T = \frac{82.14/71.875 - 1}{1.70 \times 10^{-4}} \approx 840°C$$

Steady temperature $= 27 + 840 = 867°C$

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