Question

An electric space heater has a Nichrome heating element with a resistance of 13 at 20°C. When 120 V are applied, the electric current heats the Nichrome wire to 1030°C. (a) What is the initial current drawn by the cold heating element? A (b) What is the resistance of the heating element at 1030°C? (c) What is the operating wattage of this heater? kW

Answer 1

(a) Reistance of Nichrome at 20 deg C, R = 13

Voltage, V = 120 V

So, initial current drawn by the cold heating element = V/R = 120 / 13 = 9.23 A

(b)  Here, To = 20 deg C, Tf = 1030 deg C

So, resistance of heating element at 1030 deg C -

Rf = Ro(1+(resistivity of Nichrome)(Tf-To))

Where -

Rf is the final resistance, Ro is the initial resistance
Tf is the final temp while To is the initial temp
Resistivity of nochrome = 0.0004  /deg C

=> Rf = 13* (1+0.0004 (1030 - 20))

=> Rf= 13 + 5.25 = 18.25 Ohm

(c) Operating wattage of this heater = Voltage^2/ Resistance
= (120^2)/ 18.25 = 789.0 W (Answer)