# 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, I1 = 3.2 A

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

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

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

Steady state value of the current, I2 = 2.8 A

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

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

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

Initial temperature of nichrome, T1= 27.0°C

Study state temperature reached by nichrome = T2

Tcan 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