A 1.0kW room-heater is to operate from a 230V mains supply. The heating element is to be fabricated from a wire of uniform cross-section and fixed length L. Two alternative materials are available:
Copper: ρCu=1.7×10−8Ωm at 20∘C
Nichrome: ρNiCr=1.1×10−6Ωm at 20∘C
Assume that the operating temperature remains close to 20∘C for the purpose of this calculation.
Answer the following:
(i) Determine the resistance that the heating element must possess in order to deliver the stated power at the given voltage.
(ii) Show that, for the chosen length L, the ratio of the required cross-sectional areas of copper and nichrome wires is equal to ρCu/ρNiCr.
(iii) Calculate the numerical value of this ratio.
(iv) Using the results of parts (i)–(iii), explain quantitatively which material is more suitable for the heater element and why.