A heating element using nichrome is connected to a 220 V supply. In...

Question

A heating element using nichrome is connected to a 220 V supply. Initially it draws a current of 2.9 A. After some time, the current attains a steady value of 2.5 A. Find the steady temperature of the heating element if the room temperature is 27 C. The temperature coefficient of resistance of nichrome is $1.7 	imes 10^{-4}$ $C^{-1}$.

Accepted Answer

Cold resistance: $R_0=\dfrac{V}{I_0}=\dfrac{220}{2.9}\approx75.86\ \Omega$ at $T_0=27°C$

Hot (steady) resistance: $R=\dfrac{V}{I}=\dfrac{220}{2.5}=88\ \Omega$

Using $R=R_0[1+\alpha(T-T_0)]$:

$$88=75.86[1+1.7\times10^{-4}(T-27)]$$

$$\frac{88}{75.86}=1.160=1+1.7\times10^{-4}(T-27)$$

$$T-27=\frac{0.160}{1.7\times10^{-4}}\approx941°C$$

$$T\approx968°C$$

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