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}.

#### 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} = `"V"/"I"`

= `230/3.2`

= 71.87 Ω

Steady state value of the current, I_{2} = 2.8 A

Resistance at the steady state = R_{2}, which is given as

R_{2} = `230/2.8`

= 82.14 Ω

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,

α = `("R"_2 - "R"_1)/("R"_1("T"_2 - "T"_1))`

T_{2} − 27°C = `(82.14 - 71.87)/(71.87 xx 1.7 xx 10^-4)` = 840.5

T_{2} = 840.5 + 27 = 867.5°C

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