# Aheating element using nichrome connected to a 230 V supply draws an initial current of 3.2 A which settles after a few seconds toa steady value of 2.8 A.

**Question:**

Aheating element using nichrome connected to a 230 V supply draws an initial current of 3.2 A which settles after a few seconds toa 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.

**Solution:**

Supply voltage,* V* = 230 V

Initial current drawn, *I*1 = 3.2 A

Initial resistance = *R*1, which is given by the relation,

$R_{1}=\frac{V}{I}$

$=\frac{230}{3.2}=71.87 \Omega$

Steady state value of the current, *I*2 = 2.8 A

Resistance at the steady state = *R*2, which is given as

$R_{2}=\frac{230}{2.8}=82.14 \Omega$

Temperature co-efficient of nichrome, *α* = 1.70 × 10−4 °C −1

Initial temperature of nichrome, *T*1= 27.0°C

Study state temperature reached by nichrome = *T*2

*T*2 can be obtained by the relation for *α*,

$\alpha=\frac{R_{2}-R_{1}}{R_{1}\left(T_{2}-T_{1}\right)}$

$T_{2}-27^{\circ} \mathrm{C}=\frac{82.14-71.87}{71.87 \times 1.7 \times 10^{-4}}=840.5$

$T_{2}=840.5+27=867.5^{\circ} \mathrm{C}$

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